nLab Richard Garner

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Selected writings

On weak factorization systems such as for cofibrantly generated model categories:

• R. Garner, Cofibrantly generated natural weak factorisation systems, arXiv:math.CT/0702290.

On the small object argument:

• Richard Garner, Understanding the small object argument, Applied Cat. Structures, arXiv:math.CT/0712.0724.

On infinity-groupoid/omega-groupoid-structure on types in homotopy type theory:

• Benno van den Berg, Richard Garner, Types are weak omega-groupoids, Proceedings of the London Mathematical Society 102 2 (2011) 370-394 [arXiv:0812.0298, doi:10.1112/plms/pdq026]

On dependent product types and function extensionality:

• Richard Garner, On the strength of dependent products in the type theory of Martin-Löf, Annals of Pure and Applied Logic 160 1 (2009) 1-12 [arXiv:0803.4466, doi:10.1016/j.apal.2008.12.003]

On 2-type theory

• Richard Garner, Two-dimensional models of type theory, Mathematical structures in computer science 19.4 (2009): 687-736 (doi:10.1017/S0960129509007646,pdf)

On ionads:

• Richard Garner, Ionads, J. Pure Appl. Algebra 216 (2012), no. 8-9, 1734–1747. (arXiv) (doi) (author-archived version of published copy)

On adhesive categories:

• Richard Garner, Steve Lack: On the axioms for adhesive and quasiadhesive categories, Theory and Applications of Categories, 27 3 (2012) 27-46 [arXiv:1108.2934, tac:27-03]

On the categorical semantics of dependent type theory with function types in locally cartesian closed categories (see at relation between category theory and type theory):

• Pierre-Louis Curien, Richard Garner, Martin Hofmann, Revisiting the categorical interpretation of dependent type theory, Theoretical Computer Science 546 21 (2014) 99-119 [doi:10.1016/j.tcs.2014.03.003, pdf]

On transferred model structures:

• Richard Garner, Magdalena Kedziorek, Emily Riehl, Lifting accessible model structures, J. Topology 13 1 (2020) 59-76 [arXiv:1802.09889, doi:10.1112/topo.12123]

category: people