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

Double clubs
Cahiers de Topologie et Géométrie Différentielle Catégoriques 47 (2006), no. 4, 261–317.

Polycategories via pseudodistributive 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 lowdimensional 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 MartinLöf
Annals of Pure and Applied Logic 160 (2009), no.1, pages 1–12.

A homotopytheoretic universal property of Leinster's operad for weak ωcategories
Mathematical Proceedings of the Cambridge Philosophical Society 147 (2009), no. 3, pages 615–628.

Twodimensional 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 ωgroupoids (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 14211426.

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 PierreLouis Curien & Martin Hofmann)
Theoretical Computer Science 546 (2014), pages 99–119.

Twodimensional regularity and exactness (with John Bourke)
Journal of Pure and Applied Algebra 218 (2014), no. 7, pages 1346–1371.

Lawvere theories, finitary monads and Cauchycompletion
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, in press.

Algebraic weak factorisation systems II: categories of weak
maps (with John Bourke)
Journal of Pure and Applied
Algebra, in press.

Enriched categories as a free cocompletion (with
Michael Shulman)
Under review.

When coproducts are biproducts (with Daniel
Schaeppi)
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 2015–05–07