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 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 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 KTheory 31 (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 monadLawvere theory
correspondence (with John Power)
Logical Methods in Computer Science 14 (2018).

Bousfield localisation and colocalisation of onedimensional
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 2Segal 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 costructurecosemantics 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.

Monoidal Kleisli bicategories and the arithmetic product of
coloured symmetric sequences (with Nicola Gambino and
Christina Vasilakopoulou)
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 2022–11–18