Richard Garner
I am an ARC Australian Research Fellow
and Senior Lecturer 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.
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 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, in press.

Orientals and cubes, inductively (with Mitchell
Buckley)
Under review.

Coalgebras governing both weighted Hurwitz products and their
pointwise transforms (with Ross Street)
Under
review.

Hochschild homology, lax codescent, and duplicial
structure (with Stephen Lack and Paul Slevin)
Under review.

Shapely monads and analytic functors (with Tom Hirschowitz)
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 2015–11–25