Richard Garner
I am an Associate Professor in the
Mathematics department at Macquarie University, Sydney. My research
interests are in category theory and its applications to logic,
topology, geometry and computer science.
Email:
CV: download here.
I would happily receive papers from you
in my capacity as an editor for:
Publications
-
Double clubs Cahiers de Topologie et
Géométrie Différentielle
Catégoriques 47 (2006), no. 4, 261–317.
-
Polycategories via pseudo-distributive laws
Advances in Mathematics 218 (2008), no. 3, 781–827.
-
The identity type weak factorisation system (with
Nicola Gambino) Theoretical Computer Science 409 (2008),
no. 3, pages 94–109.
-
The low-dimensional structures formed by
tricategories (with Nick Gurski) Mathematical
Proceedings of the Cambridge Philosophical Society 146 (2009),
no. 3, pages 551–589.
-
Understanding the small object argument Applied
Categorical Structures 17 (2009), no. 3, pages 247–285.
-
On the strength of dependent products in the type theory of
Martin-Löf Annals of Pure and Applied Logic
160 (2009), no.1, pages 1–12.
-
A homotopy-theoretic universal property of Leinster's operad
for weak ω-categories Mathematical
Proceedings of the Cambridge Philosophical Society 147 (2009),
no. 3, pages 615–628.
-
Two-dimensional models of type theory
Mathematical Structures in Computer Science 19 (2009), no. 4,
pages 687–736.
-
Variable binding, symmetric monoidal closed theories, and
bigraphs (with Tom Hirschowitz & Aurélien
Pardon) Lecture Notes in Computer Science 5710 (2009),
pages 321–337.
-
Homomorphisms of higher categories Advances in
Mathematics 224 (2010), no. 6, pages 2269–2311.
-
Types are weak ω-groupoids (with Benno van den
Berg) Proceedings of the London Mathematical Society 102
(2011), no. 2, pages 370–394.
-
Topological and simplicial models of identity types
(with Benno van den Berg) Transactions of the ACM on
Computational Logic 13 (2012), no. 1, pages 3:1–3:44.
-
Lex colimits (with Stephen Lack) Journal of Pure
and Applied Algebra 216 (2012), no. 6, pages 1372–1396.
-
Grothendieck quasitoposes (with Stephen Lack)
Journal of Algebra 355 (2012), no. 1, pages 111–127.
-
Remarks on exactness notions pertaining to
pushouts Theory and Applications of Categories 27
(2012), no. 1, pages 2–9.
-
An abstract view on syntax with sharing Journal
of Logic and Computation 22 (2012), no. 6, pages
1427–1452.
-
Ionads Journal of Pure and Applied Algebra 216
(2012), no. 8–9, pages 1734–1747.
-
On the axioms for adhesive and quasiadhesive
categories (with Stephen Lack) Theory and
Application of Categories 27 (2012), no. 3, pages 27–46.
-
On semiflexible, flexible and pie algebras (with John
Bourke) Journal of Pure and Applied Algebra 217 (2013), no.
2, pages 293–321.
-
A characterisation of algebraic exactness
Journal of Pure and Applied Algebra 217 (2013), no. 8, pages
1421--1426.
-
Restriction categories as enriched categories (with
Robin Cockett) Theoretical Computer Science 523 (2014),
pages 37–55.
-
Revisiting the categorical interpretation of dependent type
theory (with Pierre-Louis Curien & Martin Hofmann)
Theoretical Computer Science 546 (2014), pages 99–119.
-
Two-dimensional regularity and exactness (with John
Bourke) Journal of Pure and Applied Algebra 218 (2014), no.
7, pages 1346–1371.
-
Lawvere theories, finitary monads and
Cauchy-completion Journal of Pure and Applied
Algebra 218 (2014), no. 11, pages 1973–1988.
-
Topological functors as total categories Theory
and Applications of Categories 29 (2014), no. 15, pages
406–421.
-
Diagrammatic characterisation of enriched absolute
colimits Theory and Applications of Categories 29
(2014), no. 26, pages 775–780.
-
Combinatorial structure of type dependency
Journal of Pure and Applied Algebra 219 (2015), no. 6, pages
1885–1914.
-
The Catalan simplicial set (with Mitchell Buckley,
Stephen Lack and Ross Street) Mathematical Proceedings of
the Cambridge Philosophical Society 158 (2015), no. 2, pages
211–222.
-
The Isbell monad Advances in Mathematics 274
(2015), pages 516–537.
-
Algebraic weak factorisation systems I: accessible
AWFS (with John Bourke) Journal of Pure and
Applied Algebra 220 (2016), pages 108–147.
-
Algebraic weak factorisation systems II: categories of weak
maps (with John Bourke) Journal of Pure and Applied
Algebra 220 (2016), pages 148–174.
-
Commutativity (with Ignacio López Franco)
Journal of Pure and Applied Algebra 220 (2016), pages 1707–1751.
-
Enriched categories as a free cocompletion (with
Michael Shulman) Advances in Mathematics 289 (2016), pages 1–94.
-
When coproducts are biproducts (with Daniel
Schäppi) Mathematical Proceedings of the Cambridge
Philosophical Society 161 (2016), pages 47–51.
-
Orientals and cubes, inductively (with Mitchell
Buckley) Advances in Mathematics 303 (2016), pages 175–191.
-
Coalgebras governing both weighted Hurwitz products and their
pointwise transforms (with Ross Street) Bulletin
of the Belgian Mathematical Society 23 (2016), pages 643–666.
-
Hochschild homology, lax codescent, and duplicial
structure (with Stephen Lack and Paul Slevin)
Annals of K-Theory 3-1 (2018), pages 1–31.
-
An embedding theorem for tangent categories
Advances in Mathematics 323 (2018), pages 668–687.
-
Shapely monads and analytic functors (with Tom Hirschowitz)
Journal of Logic and Computation 28 (2018), pages 33–83.
-
An enriched view on the extended finitary monad-Lawvere theory
correspondence (with John Power)
Logical Methods in Computer Science 14 (2018).
-
Bousfield localisation and colocalisation of one-dimensional
model categories (with Scott Balchin)
Applied Categorical Structures 27 (2019), pages 1–21.
-
Monads and theories (with John Bourke)
Advances in Mathematics 351 (2019), pages 1024–1073.
-
Lifting accessible model structure (with Magdalena
Kedziorek and Emily Riehl)
Journal of Topology 13 (2020), pages 59–76.
-
Cocompletion of restriction categories (with Daniel Lin)
Theory and Applications of Categories 35 (2020), pages 809–844.
-
The Vietoris monad and weak distributive laws
Applied Categorical Structures 28 (2020), pages 339–354.
-
Ultrafilters, finite coproducts and locally connected classifying toposes
Annals of Pure and Applied Logic 171 (2020), 29 pages.
-
Every 2-Segal space is unital (with Matthew Feller,
Joachim Kock, May Proulx and Mark Weber)
Communications in Contemporary Mathematics 23 (2021), pages 1–6.
-
Operadic categories and décalage (with Joachim Kock
and Mark Weber)
Advances in Mathematics 377 (2021), pages 1–23.
-
Generalising the étale groupoid–complete pseudogroup
correspondence (with Robin Cockett)
Advances in Mathematics 392 (2021), pages 1–79.
-
Cartesian differential categories as skew enriched
categories (with JS Lemay)
Applied Categorical Structures 29 (2021), pages 1099–1150.
-
An essential local geometric morphism which is not locally
connected though its inverse image part is an exponential
ideal (with Thomas Streicher)
Theory and Application of Categories 26 (2021), pages 908–913.
-
Stream processors and comodels
in 9th Conference on Algebra and Coalgebra in
Computer Science (CALCO 2021), Leibniz International Proceedings
in Informatics 211 (2021), 17 pages.
-
The costructure--cosemantics adjunction for comodels of
computational effects
Mathematical Structures in Computer Science (2021), to appear.
-
Hypernormalisation, linear exponential monads and the Giry tricocycloid
Under review.
-
Inner automorphisms of groupoids
Under review.
Other material
-
Cofibrantly generated natural weak factorisation systems
Uppsala University Department of Mathematics Technical Report 2007:13.
-
Factorisation axioms for type theory
Notes for talk given at "Identity Types – Topological and
Categorical Structure" (Uppsala, Nov 2006).
-
Polycategories
PhD Thesis, 2006.
-
Three investigations into linear logic
First year PhD report, 2005.
Last edited 2018–11–09