Publications of Ross Street

 

0. PhD Thesis: Homotopy Classification of Filtered Complexes, University of Sydney, August 1968.

1. (with E. Dubuc) Dinatural transformations, Lecture Notes in Math. 137 (1970) 126--137; MR43#313.

2. Projective diagrams of interlocking sequences, Illinois J. Math. 15 (1971) 429--441; MR43#4881.

3. The formal theory of monads, J. Pure Appl. Algebra 2 (1972) 149--168; MR45#8701.

4. Two constructions on lax functors, Cahiers de topologie et g\'eom\'etrie diff\'erentielle 13 (1972) 217--264; MR50#436.

5. Homotopy classification of filtered complexes, J. Australian Math. Soc. 15 (1973) 298--318; MR49#5135.

6. (with R.F.C. Walters) The comprehensive factorization of a functor, Bulletin American Math. Soc. 79 (1973) 936--941; MR49#10753.

7. (with G.M. Kelly) Review of the elements of 2-categories, Lecture Notes in Math. 420 (1974) 75--103; MR50#10010.

8. Fibrations and Yoneda's lemma in a 2-category, Lecture Notes in Math. 420 (1974) 104--133; MR53#585.

9. Elementary cosmoi I, Lecture Notes in Math. 420 (1974) 134--180; MR50#7290.

10. Limits indexed by category-valued 2-functors, J. Pure Appl. Algebra 8 (1976) 149--181; MR53#5695.

11. Internally complete 2-categories, Notices American Math. Soc. 23#5 (Aug.1976) Abstract 737-18-7.

12. (with R.F.C. Walters) Yoneda structures on 2-categories, J. Algebra 50 (1978) 350--379; MR57#3214.

13. Cosmoi of internal categories, Transactions American Math. Soc. 258 (1980) 271--318; MR82a:18007.

14. Fibrations in bicategories, Cahiers de topologie et g\'eom\'etrie diff\'erentielle 21 (1980) 111--160; MR81f:18028.

15. (with W. Tholen, M. Wischnewsky, and H. Wolff) Semi-topological functors III: lifting of monads and adjoint functors, J. Pure Appl. Algebra 16 (1980) 299--314; MR81g:18003.

16. Notions of topos, Bulletin Australian Math. Soc. 23 (1981) 199--208; MR83a:18014.

17. Conspectus of variable categories, J. Pure Appl. Algebra 21 (1981) 307--338; MR84i:18006.

18. [see 85] Cauchy characterization of enriched categories, Rendiconti del Seminario Matematico e Fisico di Milano 51 (1981) 217--233; MR85e:18006; pdf

19. Two dimensional sheaf theory, J. Pure Appl. Algebra 23 (1982) 251--270; MR83d:18014.

20. Characterization of bicategories of stacks, Lecture Notes in Math. 962 (1982) 282--291; MR84d:18006.

21. Enriched categories and cohomology, Quaestiones Math. 6 (1983) 265--283; MR85e:18007.

22. (with R. Betti, A. Carboni, and R. Walters) Variation through enrichment, J. Pure Appl. Algebra 29 (1983) 109--127; MR85e:18005. Amplification of the Proof of Proposition 5.

23. Absolute colimits in enriched categories, Cahiers de topologie et g\'eom\'etrie diff\'erentielle 24 (1983) 377--379; MR85i:18001.

24. The family approach to total cocompleteness and toposes, Transactions American Math. Soc. 284 (1984) 355--369; MR85f:18003.

25. Homotopy classification by diagrams of interlocking sequences, Math. Colloquium University of Cape Town 13 (1984) 83--120; MR86i:55025; pdf.

26. (with A. Carboni and S. Kasangian) Bicategories of spans and relations, J. Pure Appl. Algebra 33 (1984) 259--267; MR86f:18013.

27. (with A. Carboni) Order ideals in categories, Pacific J. Math. 124 (1986) 275--288; MR88e:18005.

28. (with S. Schanuel) The free adjunction, Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques 27 (1986) 81--83; MR87f: 18005.

29. (with B.J. Day) Categories in which all strong generators are dense, J. Pure Appl. Algebra 43 (1986) 235--242; MR88m:18013.

30. The algebra of oriented simplexes, J. Pure Appl. Algebra 49 (1987) 283--335; MR89a:18019; (2.2Mb pdf; see [52] for a correction).

31. Correction to "Fibrations in bicategories", Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques 28 (1987) 53--56; MR88i: 18004.

32. (with D. Schumacher) Some parametrized categorical concepts, Communications in Algebra 16 (1988) 2313--2347; MR89k:18001.

33. Fillers for nerves, Lecture Notes in Math. 1348 (1988) 337--341; MR89m:18011.

34. (with B.J. Day) Localisation of locally presentable categories, J. Pure Appl. Algebra 58 (1989) 227-- 233; MR90g:18012.

35. (with G.J. Bird, G.M. Kelly, and A.J. Power) Flexible limits for 2-categories, J. Pure Appl. Algebra 61 (1989) 1--27; MR91a:18009.

36. (with B.J. Day) Localisation of locally presentable categories II, J. Pure Appl. Algebra 63 (1990) 225--229; MR91h:18007.

37. (with A. Joyal) The geometry of tensor calculus I, Advances in Math. 88 (1991) 55--112; MR92d:18011.

38. (with A. Joyal) Tortile Yang-Baxter operators in tensor categories, J. Pure Appl. Algebra 71 (1991) 43--51; MR92e:18006.

39. Quantum Groups : an entree to modern algebra (Notes from a Graduate Lecture Course March-June 1990; nearly all available as html or ps).

40. (with A. Joyal) An introduction to Tannaka duality and quantum groups; Part II of Category Theory, Proceedings, Como 1990 (Editors A. Carboni, M.C. Pedicchio and G. Rosolini) Lecture Notes in Math. 1488 (Springer-Verlag Berlin, Heidelberg 1991) 411--492; MR93f:18015.

41. Parity complexes, Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques 32 (1991) 315--343; MR93f:18014 (also see [52] below and Simon Forest's paper at http://arxiv.org/abs/1903.00282).

42. (with A. Joyal) Pullbacks equivalent to pseudopullbacks, Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques  34 (1993) 153--156; MR94a:18004.

43. (with G. Janelidze and D. Schumacher) Galois theory in variable categories, Applied Categorical Structures 1 (1993) 103--110; MR94k:18011.

44. (with A. Joyal) Braided tensor categories, Advances in Math. 102 (1993) 20--78; MR94m:18008; for earlier version see "Other widely circulated output ix" below.

45. Categorical structures, Handbook of Algebra Volume 1 (editor M. Hazewinkel; Elsevier Science, Amsterdam 1996; ISBN 0 444 82212 7) 529--577; pdf.

46. (with A. Carboni, S. Johnson and D. Verity) Modulated bicategories, J. Pure Appl. Algebra 94 (1994) 229--282; MR96f:18008.

47. (with R. Gordon and A.J. Power) Coherence for tricategories, Memoirs of the American Math. Society 117 (1995) Number 558 (ISBN 0-8218-0344-1); MR96j:18002.

48. Higher categories, strings, cubes and simplex equations, Applied Categorical Structures 3 (1995) 29--77 & 303; MR96b:18009; pdf.

49. (with A. Joyal) The category of representations of the general linear groups over a finite field, J. Algebra 176 (3) (1995) 908--946; MR96k:20082.

50. Ideals, radicals, and structure of additive categories, Applied Categorical Structures 3 (1995) 139--149; MR96e:18003; pdf.

51. (with A. Joyal and D. Verity) Traced monoidal categories, Mathematical Proceedings of the Cambridge Philosophical Society 119 (3) (1996) 425--446; MR96m:18014. [Related documents: Amy Young’s project and http://dx.doi.org/10.1017/S0305004109002606].

52. Parity complexes: corrigenda, Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques 35 (1994) 359--361; MR95j:18005.

53. (with A. Joyal) The geometry of tensor calculus II (draft document, also see (xii) below).

54. (with D. Verity) Surface diagrams for tricategories; superseded by

M. McIntyre and T. Trimble, The geometry of Gray-categories, Advances in Math. (withdrawn; but see http://ncatlab.org/toddtrimble/published/Surface+diagrams).

 

55. (with B. Day) Kan extensions along promonoidal functors, Theory and Applications of Categories 1 (4) (1995) 72--78; MR96a:18003.

56. (with P. Freyd) On the size of categories, Theory and Applications of Categories 1 (9) (1995) 174--178; MR96m:18004.

57. Low-dimensional topology and higher-order categories, Proceedings of CT95, Halifax, 9-15 July 1995; pdf.

58. Fusion operators and cocycloids in monoidal categories, Applied Categorical Structures 6 (2) (Special Issue on ``Quantum Groups, Hopf Algebras and Category Theory'', ed. A. Verschoren, 1998) 177--191; MR99d:18008; pdf.

59. Descent theory (notes of three lectures presented at Oberwolfach, September 1995); pdf.

60. (with B.J. Day) Monoidal bicategories and Hopf algebroids, Advances in Math. 129 (1997) 99--157; MR99f:18013; Remark on Example 11.

61. (with Renato Betti and Dietmar Schumacher) Factorizations in bicategories, Dipartimento di Matematica, Politecnico di Milano, n. 22/R (May 1999); draft 20 Nov. 1997.

62. (with P.J. Freyd, P.W. O'Hearn, A.J. Power, M. Takeyama, and R.D. Tennent) Bireflectivity, Theoretical Computer Science 228 (1-2) (1999) 49--76; MR2000i:68110.

63. The quantum double and related constructions, J. Pure Appl. Algebra 132 (1998) 195--206; MR99e:16054.

64. The role of Michael Batanin’s monoidal globular categories, in: ``Higher Category Theory'' (editors E. Getzler and M. Kapranov) Contemporary Mathematics 230 (A.M.S. 1998) 99--116; MR 2000a:18006.

65. (see [110]) Parenthetic remarks (preprint, pdf).

66. (with M. Batanin) The universal property of the multitude of trees, J. Pure Appl. Algebra 154 (2000) 3--13; MR2001f:18014.

67. (with G. Janelidze) Galois theory in symmetric monoidal categories, Macquarie Mathematics Report 98/235 (April 1998); preliminary announcement in Seminarberichte aus dem Fachbereich Mathematik, Band 63, Teil 3 (1998) 365-375; Journal of Algebra 220 (1999) 174--187; MR2000h:18017.

68. Braids among the groups Seminarberichte aus dem Fachbereich Mathematik, Band 63, Teil 5 (1998) 699--703.

69. The petit topos of globular sets, J. Pure Appl. Algebra 154 (2000) 299--315; MR2001f:18008. A point of correction.

70. (with G.M. Kelly, A. Labella and V. Schmitt) Categories enriched on two sides, J. Pure Appl. Algebra 168 (1) (8 March 2002) 53--98; MR2003f:18006 pdf.

71. (with S. Lack) The formal theory of monads II, J. Pure Appl. Algebra 175 (1-3) (2002) 243--265; MR2003m:18007 ps.gz.

72. (with B.J. Day) Lax monoids, pseudo-operads, and convolution, in: "Diagrammatic Morphisms and Applications", Contemporary Mathematics 318 (AMS; ISBN 0-8218-2794-4; April 2003) 75--96; MR2004c:18011; pdf.

73. (with J. Bichon) Militaru's D-equation in monoidal categories, Applied Categorical Structures 11 (2003) 337--357; MR2004f:18011; ps.gz.

74. Functorial calculus in monoidal bicategories, Applied Categorical Structures 11 (2003) 219--227; MR2004f:18010; pdf.

75. (with B.J. Day and P. McCrudden) Dualizations and antipodes, Applied Categorical Structures 11 (2003) 229--260; MR2004b:18013; pdf.

76. Weak omega-categories, in: ``Diagrammatic Morphisms and Applications'', Contemporary Mathematics 318 (AMS; ISBN 0-8218-2794-4; April 2003) 207--213; MR 2004c:18008; pdf.

77. (with B.J. Day) Abstract substitution in enriched categories, J. Pure Appl. Algebra 179 (2003) 49--63; MR2004d:18008; pdf.

78. (with A. Davydov) Roots of unity as a Lie algebra, Georgian Mathematical Journal 9(4) (2002) 683--690; MR2004c:18010 pdf.

79. (with B.J. Day) Quantum categories, star autonomy, and quantum groupoids, in "Galois Theory, Hopf Algebras, and Semiabelian Categories", Fields Institute Communications 43 (American Math. Soc. 2004) 187--226 (preprint pdf or math.CT/0301209).

80. Categorical and combinatorial aspects of descent theory, Applied Categorical Structures 12 (2004) 537--576 (preprint at pdf and math.CT/0303175; also see the supplementary expository article [o] below); MR2005h:18022.

81. The monoidal centre as a limit, Theory and Applications of Categories 13(13) (ed. G. Janelidze, S. Lack, F.W. Lawvere, E.M. Vitale and R.J. Wood: volume dedicated to Aurelio Carboni for his 60th birthday; 2004) 184--190 (old preprint pdf or even older version at math.CT/0304053); MR2005h:18027.

82. (with R. Buchweitz and A. Davydov) The Gerstenhaber homotopy in a monoidal bicategory (in preparation).

83. Frobenius monads and pseudomonoids, J. Math. Physics 45(10) (October 2004) 3930--3948 (old preprint pdf); MR2005h:18026.

84. Monoidal actions, enriched categories, and convolution (in preparation).

85. [see 18] Cauchy characterization of enriched categories, Reprints in Theory and Applications of Categories 4 (2004) 1--16.

86. An Australian conspectus of higher categories, in: Towards Higher Categories, edited by John C. Baez and J. Peter May, The IMA Volumes in Mathematics and its Applications, Volume 152 (Springer, 2009) 237--264 (arising from the 2004 Summer Program: n-Categories: Foundations and Applications, 1-18 June 2004 at the IMA of the University of Minnesota, Minneapolis); available at pdf.

87. (with Brian Day and Elango Panchadcharam) Lax braidings and the lax centre, in ``Hopf Algebras and Generalizations'', Contemporary Mathematics 441 (2007; pdf; details) 1--17.

 

88. [see 21] Enriched categories and cohomology with author commentary, Reprints in Theory and Applications of Categories 14 (2005) 1--18.

89. (with Brian Day) Centres of monoidal categories of functors, in ``Categories in Algebra, Geometry and Mathematical Physics'', Contemporary Mathematics 431 (2007) 187--202 (details).

90. [see 39] Quantum Groups: a path to current algebra, Australian Math. Society Lecture Series 19 (Cambridge University Press; 18 January 2007; ISBN-978-0-521-69524-4).

91. (with Brian Day and Elango Panchadcharam) On centres and lax centres for promonoidal categories, Colloque International ``Charles Ehresmann : 100 ans Universit\'e de Picardie Jules Verne \`a Amiens 7-8-9 Octobre 2005'' <pdf>.

92. (with Eduardo Dubuc) A construction of 2-filtered bicolimits of categories, Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques 47(2) (2006) 83--106 <arXiv:0605304>; Corrections 62(2) (2021) 239--242.

93. (with Elango Panchadcharam) Mackey functors on compact closed categories, Journal of Homotopy and Related Structures 2(2) (2007) 261--293; http://arxiv.org/abs/0706.2922.

94. (with Elango Panchadcharam) Pullback and finite coproduct preserving functors between categories of permutation representations, Theory and Applications of Categories 16(28) (2006) 771--784 <pdf>.

95. (with Elango Panchadcharam) Pullback and finite coproduct preserving functors between categories of permutation representations: corrigendum and addendum, Theory and Applications of Categories, 18(5) (2007) 151--156 <pdf>.

96. (with Craig Pastro) Weak Hopf monoids in braided monoidal categories, Algebra and Number Theory 3(2) (2009) 149--207; http://pjm.math.berkeley.edu/ant/2009/3-2/index.xhtml.

97. (with Craig Pastro) Closed categories, star-autonomy, and monoidal comonads, Journal of Algebra 321(11) (1 June 2009) 3494--3520 (Special Issue in Honor of Gus Lehrer; http://arxiv.org/abs/0712.0418).

 

98. (with Craig Pastro) Doubles for monoidal categories, Theory and Applications of Categories 21(4) (2008) 61--75; pdf  (also http://arxiv.org/abs/0711.1859).

99. (with Ignacio Lopez-Franco and Richard Wood) Duals invert, Applied Categorical Structures 19(1) (February 2011) 321--362 (published online 8 September 2009: (special volume in memory of Max Kelly).

100. (with Ronald Brown) Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product, Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques 52(3) (2011) 188--208 (also see http://arxiv.org/abs/1009.5609).

101. Weak distributive laws, Theory and Applications of Categories 22(12) (2009) 313--320; <http://www.tac.mta.ca/tac/volumes/22/12/22-12.pdf>.

102. (with Micah Blake McCurdy) What separable Frobenius monoidal functors preserve, Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques  51(1) (2010) 29--50 (volume celebrating Francis Borceux's '60th birthday); http://arxiv.org/pdf/0904.3449v1).

103. (with Dimitri Chikhladze and Stephen Lack) Hopf monoidal comonads, Theory and Applications of Categories 24(19) (2010) 554--563 (http://www.tac.mta.ca/tac/volumes/24/19/24-19.pdf ; also see http://arxiv.org/pdf/1002.1122).

104. (with Dominic Verity) The comprehensive factorization and torsors, Theory and Applications of Categories 23(3) (2010) 42--75; (in the volume celebrating Dominique Bourn's 60th birthday; pdf).

105. (with Gabriella Boehm and Stephen Lack) Weak bimonads and weak Hopf monads, Journal of Algebra 328 (2011) 1--30 (published online at http://dx.doi.org/10.1016/j.jalgebra.2010.07.032; also see http://arxiv.org/abs/1002.4493).

106. (with Thomas Booker) Torsors, herds and flocks, Journal of Algebra 330 (2011) 346--374 (also see http://arxiv.org/abs/0912.4551).

107. (with Gabriella Boehm and Stephen Lack) On the 2-categories of weak distributive laws, Communications in Algebra 39(12) (2011) 4567--4583 (dedicated to Miriam Cohen; also see arXiv:1009.3454).

108. (with Gabriella Boehm, Thomas Booker, Brian Day and Stephen Lack) Separable enriched categories and absolute ends (in preparation).

109. (with Gabriella Boehm and Stephen Lack) Idempotent splittings, colimit completions, and weak aspects of the theory of monads, Journal of Pure and Applied Algebra 216(2) (2012) 385--403; also see arXiv:1102.4931.

110. (see [65]) Parenthetic remarks, in ``Associahedra, Tamari Lattices and Related Structures'', Tamari Memorial Festschrift, editors F. Mueller-Hoissen, J. Pallo and J. Stasheff, Progress in Mathematics 299 (Birkhauser, 29 June 2012) 251--268.

111. (with Thomas Booker) Tannaka duality and convolution for duoidal categories, Theory and Applications of Categories 28(6) (2013)166--205.

112. The core of adjoint functors, Theory and Applications of Categories 27(4) (2012) 47--64.

113. Monoidal categories in, and linking, geometry and algebra, Bulletin of the Belgian Mathematical Society – Simon Stevin 19(5) (2012) 769--821 (see http://arxiv.org/abs/1201.2991).

114. Categories in categories, and size matters, Higher Structures  1(1) (2017) 225—270.

115. (with Stephen Lack) Skew monoidales, skew warpings and quantum categories, Theory and Applications of Categories 26(15) (2012) 385--402.

116. Skew-closed categories, Journal of Pure and Applied Algebra 217(6) (June 2013) 973--988 (doi: 10.1016/j.jpaa.2012.09.020 published online 22 Oct 2012; also see http://arxiv.org/abs/1205.6522).

117. (with Stephen Lack) A skew-duoidal Eckmann-Hilton argument and quantum categories, Applied Categorical Structures 22 (2014) 789--803 (doi: 10.1007/s10485-013-9356-1; also see http://arxiv.org/abs/1210.8192).

118. (with Stephen Lack) Triangulations, orientals, and skew-monoidal categories, Advances in Math. 258 (2014) 351--396.

119. (with Mitchell Buckley, Richard Garner and Stephen Lack) The Catalan simplicial set, Mathematical Proceedings of the Cambridge Philosophical Society 158(2) (March 2015) 211--222; early version at http://arxiv.org/abs/1307.0265).

120. (with Stephen Lack) Combinatorial categorical equivalences of Dold-Kan type, Journal of Pure and Applied Algebra 219 (2015) 4343--4367; somewhat corrected version at http://arxiv.org/abs/1402.7151.

121. (with Stephen Lack) On monads and warpings, Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques 55 (2014) 244--266; pdf.

122. (with Stephen Lack) Skew-monoidal reflection and lifting theorems, Theory and Applications of Categories 30(28) (2015) 985--1000; http://arxiv.org/abs/1410.6972.

123. Kan extensions and cartesian monoidal categories, Seminarberichte Mathematik 87 (FernUniversit\"at in Hagen, 2015) 89--96; see http://arxiv.org/abs/1409.6405.

124. Pointwise extensions and sketches in bicategories, http://arxiv.org/abs/1409.6427.

125. Weighted tensor products of Joyal species, graphs, and charades, SIGMA 12 (2016) 005, 20pp; http://www.emis.de/journals/SIGMA/2016/005/.

126. (with Hans-E. Porst) Generalizations of the Sweedler dual, Applied Categorical Structures (in the volume to the memory of Horst Herrlich) 24 (2016) 619--647.

127. (with Richard Garner) Coalgebras governing both weighted Hurwitz products and their pointwise transforms, in: ``New trends in Hopf algebras and tensor categories'',  Bulletin of the Belgian Mathematical Society – Simon Stevin 23 (2016) 643--666; see http://arxiv.org/abs/1510.05323.

128.  Wreaths, mixed wreaths and twisted coactions, Tbilisi Mathematical Journal (in the volume in honour of Peter Freyd and Bill Lawvere) 10(3) (2017) 1--22.

129. (with George Janelidze) Real sets, Tbilisi Mathematical Journal (in the volume in honour of Peter Freyd and Bill Lawvere) 10(3) (2017) 23--49.

130. (with Branko Nikoli\'c) Comonadic base change for enriched categories; see http://arxiv.org/abs/1809.02356.

 

131. (with George Janelidze) Infinitary addition, real numbers, and taut monads, Applied Categorical Structures 26(5) (2018) 1047--1064.

 

132. (with Branko Nikoli\'c) Hopf rings for grading and differentials; see http://arxiv.org/abs/1806.09318.

 

133. Vector product and composition algebras in braided monoidal additive categories, Commentationes Mathematicae Universitatis Carolinae (in volume in memory of V\v{e}ra Trnkov\'a) 60(4) (2019) 581-604; also see http://arxiv.org/abs/1812.04143.

 

134. Polynomials as spans, Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques 61(2) (2020) 113--153; see http://arxiv.org/abs/1903.03890.

 

135. Span composition using fake pullbacks, Theory and Applications of Categories (in volume dedicated to Bob Rosebrugh) 36 (2021) 102--117; see http://arxiv.org/abs/1907.02695.

 

136. (see [120]; with Stephen Lack) Corrigendum to ``Combinatorial categorical equivalences of Dold-Kan type'', Journal of Pure and Applied Algebra 224 (2020) 1364--1366; pdf.

 

137. (with Kevin Coulembier and Michel van den Bergh) Freely adjoining monoidal duals, Mathematical Structures in Computer Science (2020; in volume for John Power’s 60th birthday) 1--21; (doi:10.1017/S0960129520000274; also see http://arxiv.org/abs/2004.09697).

 

138. (with Branko Nikoli\'c) Monoidal centres and groupoid-graded categories; see http://arxiv.org/abs/2010.10656.

 

139. (with Branko Nikoli\'c and Giacomo Tendas) Cauchy completeness for DG-categories, Theory and Applications of Categories 37(28) (2021) 940--963; see http://arxiv.org/abs/2012.10157.

 

140. Variation on a comprehensive theme, Theory and Applications of Categories, 37(29) (2021) 964--978; see arXiv:2104.02887.

 

141. (with Alexei Davydov) Extensions and deformation cohomology of tensor categories.

 

142. The core groupoid can suffice; see http://arxiv.org/abs/2208.11332.

 

Volumes Edited

(with George Janelidze, John MacDonald and Walter Tholen) Proceedings of CT2004 at UBC (Vancouver), Theory and Applications of Categories 15.

(with Aurelio Carboni and George Janelidze) Special Volume celebrating the 70th birthday of Professor Max Kelly, Journal of Pure and Applied Algebra 175(1-3) (8 November 2002).

(with Jawad Abuhlail, Gabriella Boehm, Tomasz Brzezinski, H. Peter Gumm, Salah-Eddine Kabbaj and Robert Wisbauer) "Interactions of Algebraic and Coalgebraic Structures (Theory and Applications)" Arabian Journal for Science and Engineering, Section C: Theme Issues 33(2 C) (December 2008).

(with Maria Manuel Clementino and Samson Abramsky) Special Issues devoted to CT2007 at Carvoeiro (Algarve, Portugal):

a)    "Topology and Homotopy" Applied Categorical Structures 17(3) (June 2009)

b)   "Semi-abelian Categories" Applied Categorical Structures 17(4) (August 2009)

c)    "Toposes and Functor Categories" Applied Categorical Structures 18(2) (April 2010)

d)   "Enriched and Higher Categories" Applied Categorical Structures 18(3) (June 2010).

(with Martin Hyland, George Janelidze, Michael Johnson, Peter Johnstone, Stephen Lack, Walter Tholen and Richard Wood) Special Issue: Dedicated to the Memory of Professor Gregory Maxwell Kelly, Applied Categorical Structures 19(1) (February 2011).

(with Marino Gran, Maria Manuel Clementino, Manuela Sobral and Walter Tholen) Special Issue celebrating the 60th birthday of George Janelidze: Applied Categorical Structures 22 (2014).

(with Bernhard Banaschewski, Maria Manuel Clementino, Eva Colebunders, George Janelidze and Walter Tholen) Special Issue dedicated to Professor Robert Lowen: Applied Categorical Structures 26(5) (2018).

Volume Dedicated

"Categories in Algebra, Geometry and Mathematical Physics", Conference and Workshop in honor of Ross Street's 60th Birthday, Macquarie University 11-16 July 2005 and Australian National University 18-21 July 2005; edited by Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack and Amnon Neeman; Contemporary Mathematics 431 (American Math. Society, 2007).

Expository Articles

a. Geometry using painting, Parabola 10 #2 (1974) 8--13.

b. Numbers from space, Reflections 7 (Math. Assoc. of NSW, 1982) 8--10.

c. An efficient construction of the real numbers, Gazette Australian Math. Soc. 12 (1985) 57--58. Click here for a full version (jointly with Vacation Scholars James Douglas, Rony Kirollos, Ben Odgers and Nguyen Hanh Vo; February 2004) including the original article. There is also the older September 2003 update.

d. The mathematics of knots, Reflections 21 (4) (Math. Assoc. of NSW, 1996) 12--21.

e. Bicategories and 2-categories, Encyclopaedia of Mathematics, Supplement II (ed. M. Hazewinkel; Kluwer Academic, 2000) 65--67.

f. Higher-dimensional categories; n-categories, Encyclopaedia of Mathematics, Supplement II (ed. M. Hazewinkel; Kluwer Academic, 2000) 254--257.

g. Consequences of splitting idempotents (November 1996, notes; pdf); Addendum

h. Branches of higher dimensional algebra, Talk at Aust Math Soc Conference at the University of Sydney (30 September 1998)

i. Rationals, reals, complexes! What next? (Blakers Lecture, National Mathematics Summer School, 18 January 1999; it is a talk about quaternions)

j. Trees, permutations and the tangent function, Reflections 27 (2) (Math. Assoc. of NSW, May 2002) 19--23; pdf and math.HO/0303267; beamer version.

k. Powerful functors; pdf

l. The 3-cocycle condition; pdf

m. Formal representation theory, Invited talk at the Fields Institute (Toronto, Canada, September 2002); audio and lecture notes.

n. Lack's lemma on comma objects.

o. Lecture at ICIAM 2003 (11 July 2003) "Categorical and combinatorial aspects of descent theory", 2003ICIAM.pdf (while this is intended to be self-contained, it is supplementary to [80] above).

p. Monoidal categories for the combinatorics of group representations; pdf

q. Frobenius algebras and monoidal categories, Lecture at the Annual Meeting of the Australian Math. Soc. (29 September 2004).

r. Bicategories

s. Group cohomology

t. Talk to Macquarie Philosophy Students' Society

u. Sculptured Journey, aMUSine Issue 8: "Journeys"

v. Duality and well pointedness

w. Euler’s polyhedron formula and Platonic solids

Book Reviews

I. Review of: J.W. Gray, Formal Category Theory: Adjointness for 2-Categories (Lecture Notes in Math. 391, Springer 1974); in Mathematical Reviews 51#8207 (April 1976) 1153.

II. Review of: Kirill Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry (London Math. Soc. Lecture Note Series No.124, Cambridge University Press 1987); in Gazette Australian Math. Soc. 16#3 (June 1989) 66--68.

III. Review of: Colin McLarty, Elementary Categories, Elementary Toposes (Oxford University Press 1992); in Zentralblatt f\"ur Mathematik 762 (12) (1993) #18001.

IV. Review of: Robert Gordon, G-Categories (Memoirs Amer. Math. Soc. 101 (1993) #482); in Mathematical Reviews MR# 93f:18003.

V. Review of: Frederick Chong and Ronald J. Andrews, A View of Mathematics: Big Picture Plus Close-ups (The Mathematical Association of New South Wales, March 1995), Gazette Australian Math. Soc. 23 (5) (1996) 214--215.

VI. Review of: David N. Yetter, Functorial knot theory: Categories of tangles, coherence, categorical deformations, and topological invariants (Series on Knots and Everything 26, World Scientific, Singapore, 2001): in Bulletin of the London Mathematical Society 35 (2003) 137--139.

VII. Review of: Tom Leinster, Higher Operads, Higher Categories, (London Math. Soc. Lecture Note Series 298, Cambridge University Press 2004); in Mathematical Reviews MR2094071.

VIII. Review of: Peter T. Johnstone, Sketches of an elephant. A topos theory compendium. I and II (Oxford Logic Guides 44; Oxford Science Publications. Oxford: Clarendon Press, 2002); in Zentralblatt f\"ur Mathematik Zbl 1071.18002.

IX. Review of: Steve Awodey, Category Theory (Oxford Logic Guides 49; Oxford University Press (2006) 256 pp.); in Zentralblatt f\"ur Mathematik Zbl 1100.18001.

X. Review of: Eckmann-Tierney eds: Seminar on Triples and Categorical Homology Theory (Repr. Theory Appl. Categ. No. 18 (2008) 303 pp.); in Mathematical Reviews MR2410935 (2009m:18005).

XI. Review of: Jean-Pierre Marquis, From a geometrical point of view. A study of the history and philosophy of category theory (Logic, Epistemology, and the Unity of Science 14: Springer, Dordrecht, 2009); in Mathematical Reviews MR2730089.

XII. Review of: John C. Baez, Aristide Baratin, Laurent Freidel and Derek K. Wise: Infinite-dimensional representations of 2-groups, (Memoirs American Math. Soc. 219(1032)); in Mathematical Reviews MR2978538.

XIII. Review of: Marco Grandis, Homological algebra. The interplay of homology with distributive lattices and orthodox semigroups. (Hackensack, NJ: World Scientific, 2012); in Zentralblatt f\"ur Mathematik Zbl 1280.18001.

XIV. Review of: Nick Gurski, Coherence in Three-Dimensional Category Theory, Cambridge Tracts in Mathematics 201 (CUP, 2013); in Zentralblatt fuer Mathematik.

XV. Review of: Daniel Sch\"appi, The Formal Theory of Tannaka Duality, Ast\'erisque 357 (Soci\'et\'e Math\'ematique de France, 2013); in Zentralblatt f\"ur Mathematik.

XVI. Paul Balmer and Ivo Dell’Ambrogio, Mackey 2-functors and Mackey 2-motives, Monographs in Math. (Eur. Math. Soc. 2020); in Mathematical Reviews MR4192744.

Speech

In celebration of Professor Chong's eightieth birthday, Reflections 24 (2) (May, 1999) 2--3.

Obituaries and biographies

Professor Frederick Chong, Gazette Austral. Math. Society 26 #4 (October 1999) 211--213; pdf.

Professor G. Maxwell Kelly, "Polymath revelled in the mystery of numbers" Sydney Morning Herald (Timelines 11 April 2007).

Professor G. Maxwell Kelly, Gazette Austral. Math. Society 34 #2 (May 2007) 94--96.

(with W. Chen and K. Matthews) Dr Peter Pleasants, Gazette Austral. Math. Society 35 #3 (July 2008) 162--165.

"Gregory Maxwell Kelly 1930-2007", Historical Records of Australian Science 21(2) (CSIRO Publishing, 2010) 237--251.

"Brian John Day 16 January 1945 - 16 June 2012", Gazette Austral. Math. Society 40 #2 (May 2013) 99--101.

Other widely circulated output

i. The universal property of the representation functor (1972).

ii. (editor, with G.M. Kelly) Abstracts of the Sydney Category Seminar 1972. (First printing at Univ. of NSW; second at Macquarie University).

iii. The calculus of modules (1976).

iv. Topos theory: Survey (1978), Notes for a senior algebra course (1978), Lectures at Monash Univ. (Jan 1974), Topic list at Christchurch New Zealand (Nov 2004).

v. The comprehensive construction of free colimits, Macquarie Math. Reports 79000 (1979).

vi. (see [104]) One-dimensional non-abelian cohomology, Macquarie Math. Reports 810024 (1981).

vii. An unpublished theorem of P.J. Freyd and R. Street discussed with attribution in [G.M. Kelly and V. Koubek, The large limits that all good categories admit, J. Pure Appl. Algebra 22 (1981) 253-263].

viii. (with B.J. Day) An additive Giraud theorem (1984).

ix. (with A. Joyal) Braided monoidal categories, Macquarie Math Reports 860081 (1986); Macquarie Math Reports 850067 (1985).

x. Gray's tensor product of 2-categories (February 1988).

xi. A construction of the Azumaya complex, on page 116 of ``The Azumaya complex of a commutative ring'' by J.W. Duskin, Lecture Notes in Math. 1348 (1988)107--117; MR90c:13003.

xii. (with A. Joyal) Planar diagrams and tensor algebra (1988).

xiii. Higher descent structures, Geometric and Logical Aspects of Descent Theory 17.09.-23.09.1995 (Tagungsbericht 38/1995, Mathematisches Forschungsinstitut Oberwolfach).

xiv. Higher-dimensional nerves (handwritten notes, 1982).

Other material.

A. (with S. Eilenberg) Rewrite systems, algebraic structures, and higher-order categories (handwritten manuscripts; for example).

B. (with G.J. Bird, G.M. Kelly and A.J. Power) Explicit formulas for the strict reflections of pseudo and lax natural transformations.

C. The Tannakian adjunction.

D. Complex functorial analysis

E. Notes on factorization

F. Complete objects relative to a theory (June 1976)

G. Understanding Steiner (8 October 1990)

I. Synthetic Plane Projective Geometry (Lecture Notes, 1971)

J. Note on Hall's Marriage Theorem

K. Skew monads