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Richard Garner

I am an ARC Australian Research Fellow in the Mathematics department at Macquarie University, Sydney. My research interests are in abstract mathematics, broadly construed, in particular in category theory and its applications to logic, topology, geometry and computer science.

Email:
CV: download here.

Publications

  1. Double clubs
    Cahiers de Topologie et Géométrie Différentielle Catégoriques 47 (2006), no. 4, 261–317.
  2. Polycategories via pseudo-distributive laws
    Advances in Mathematics 218 (2008), no. 3, 781–827.
  3. The identity type weak factorisation system (with Nicola Gambino)
    Theoretical Computer Science 409 (2008), no. 3, pages 94–109
  4. The low-dimensional structures formed by tricategories (with Nick Gurski)
    Mathematical Proceedings of the Cambridge Philosophical Society 146 (2009), no. 3, pages 551–589.
  5. Understanding the small object argument
    Applied Categorical Structures 17 (2009), no. 3, pages 247–285.
  6. 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.
  7. 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.
  8. Two-dimensional models of type theory
    Mathematical Structures in Computer Science 19 (2009), no. 4, pages 687–736.
  9. Variable binding, symmetric monoidal closed theories, and bigraphs (with Tom Hirschowitz & Aurélien Pardon)
    Lecture Notes in Computer Science 5710 (2009), pages 321–337.
  10. Homomorphisms of higher categories
    Advances in Mathematics 224 (2010), no. 6, pages 2269–2311.
  11. Types are weak ω-groupoids (with Benno van den Berg)
    Proceedings of the London Mathematical Society 102 (2011), no. 2, pages 370–394.
  12. 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.
  13. Lex colimits (with Stephen Lack)
    Journal of Pure and Applied Algebra 216 (2012), no. 6, pages 1372–1396.
  14. Grothendieck quasitoposes (with Stephen Lack)
    Journal of Algebra 355 (2012), no. 1, pages 111–127.
  15. Remarks on exactness notions pertaining to pushouts
    Theory and Applications of Categories 27 (2012), no. 1, pages 2–9.
  16. An abstract view on syntax with sharing
    Journal of Logic and Computation 22 (2012), no. 6, pages 1427–1452.
  17. Ionads
    Journal of Pure and Applied Algebra 216 (2012), no. 8–9, pages 1734–1747.
  18. On the axioms for adhesive and quasiadhesive categories (with Stephen Lack)
    Theory and Application of Categories 27 (2012), no. 3, pages 27–46.
  19. On semiflexible, flexible and pie algebras (with John Bourke)
    Journal of Pure and Applied Algebra 217 (2013), no. 2, pages 293–321.
  20. A characterisation of algebraic exactness
    Journal of Pure and Applied Algebra 217 (2013), no. 8, pages 1421--1426.
  21. Restriction categories as enriched categories (with Robin Cockett)
    Theoretical Computer Science 523 (2014), pages 37–55.
  22. Revisiting the categorical interpretation of dependent type theory (with Pierre-Louis Curien & Martin Hofmann)
    Theoretical Computer Science 546 (2014), pages 99–119.
  23. Two-dimensional regularity and exactness (with John Bourke)
    Journal of Pure and Applied Algebra 218 (2014), no. 7, pages 1346–1371.
  24. Lawvere theories, finitary monads and Cauchy-completion
    Journal of Pure and Applied Algebra 218 (2014), no. 11, pages 1973–1988.
  25. Topological functors as total categories
    Theory and Applications of Categories 29 (2014), no. 15, pages 406–421.
  26. Diagrammatic characterisation of enriched absolute colimits
    Theory and Applications of Categories 29 (2014), no. 26, pages 775–780.
  27. Combinatorial structure of type dependency
    Journal of Pure and Applied Algebra 219 (2015), no. 6, pages 1885–1914.
  28. 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.
  29. The Isbell monad
    Advances in Mathematics 274 (2015), pages 516–537.
  30. Algebraic weak factorisation systems I: accessible AWFS (with John Bourke)
    Journal of Pure and Applied Algebra, in press.
  31. Algebraic weak factorisation systems II: categories of weak maps (with John Bourke)
    Journal of Pure and Applied Algebra, in press.
  32. Enriched categories as a free cocompletion (with Michael Shulman)
    Under review.
  33. When coproducts are biproducts (with Daniel Schaeppi)
    Under review.

Other material

  1. Cofibrantly generated natural weak factorisation systems
    Uppsala University Department of Mathematics Technical Report 2007:13.
  2. Factorisation axioms for type theory
    Notes for talk given at "Identity Types – Topological and Categorical Structure" (Uppsala, Nov 2006).
  3. Polycategories
    PhD Thesis, 2006.
  4. Three investigations into linear logic
    First year PhD report, 2005.

Last edited 2015–05–07