nLab Dominic Verity

Dominic Verity is a British category theorist, based in Australia. He is an Emeritus Professor at Macquarie University.

He has worked on the theory of complicial sets and their weak analogues, which followed up on ideas of John Roberts on cohomology and, effectively, omega-category theory.

More recently he has worked with Emily Riehl on foundations of $(\infty, 1)$-category theory seen through their homotopy 2-category, and using the concept of ∞-cosmoi to capture common structure of different presentations of $(\infty, 1)$-categories.

• Departmental webpage

• Mathematics Genealogy page

Selected writings

On enriched category theory and internal categories:

• Enriched categories, internal categories and change of base Ph.D. thesis, Cambridge University (1992), reprinted as Reprints in Theory and Applications of Categories, No. 20 (2011) pp 1-266 (TAC)

Introducing the notion of traced monoidal categories:

• André Joyal, Ross Street, Dominic Verity, Traced monoidal categories, Math. Proc. Camb. Phil. Soc. 119 (1996) 447-468 [pdf, doi:10.1017/S0305004100074338]

On weak complicial sets:

• D. R. Verity, 2005, Complicial Sets , available from : arXiv:math.CT/0410412.

• D. Verity, 2006, Weak complicial sets I: basic homotopy theory , available from : arXiv:math/0604414.

• D. R. Verity, 2006, Weak complicial sets. III. Enriched and internal quasi-category theory , (in preparation).

• D. R. Verity, 2007, Weak complicial sets. II. Nerves of complicial Gray-categories , in Categories in algebra, geometry and mathematical physics , volume 431 of Contemp. Math., 441–467, Amer. Math. Soc., Providence, RI.

On comprehensive factorization systems and torsors:

• Ross Street, Dominic Verity, The comprehensive factorization and torsors, TAC 23 (2010) 42-75 [tac:23-03]

On (∞,1)-category theory via the homotopy 2-category of (∞,1)-categories of ∞-cosmoi (formal $(\infty,1)$-category theory):

• Emily Riehl, Dominic Verity, The 2-category theory of quasi-categories, Advances in Mathematics Volume 280, 6 August 2015, Pages 549-642 (arXiv:1306.5144, doi:10.1016/j.aim.2015.04.021)

• Emily Riehl, Dominic Verity, Infinity category theory from scratch, Higher Structures Vol 4, No 1 (2020) (arXiv:1608.05314, pdf)

• Emily Riehl, Dominic Verity, Elements of ∞-Category Theory, Cambridge studies in advanced mathematics 194, Cambridge University Press (2022) $[$doi:10.1017/9781108936880, ISBN:978-1-108-83798-9, pdf$]$

On (∞,1)-functors and (∞,1)-monads:

• Emily Riehl, Dominic Verity, Homotopy coherent adjunctions and the formal theory of monads, Advances in Mathematics, Volume 286, 2 January 2016, Pages 802-888 (arXiv:1310.8279, doi:10.1016/j.aim.2015.09.011)

On Reedy model structures via weighted colimits:

• Emily Riehl, Dominic Verity, The theory and practice of Reedy categories, Theory and Applications of Categories 29 9 (2014) 256-301 [tac:29-09,arXiv:1304.6871]

On the Yoneda lemma for (∞,1)-categories:

• Emily Riehl, Dominic Verity, Fibrations and Yoneda’s lemma in an $\infty$-cosmos, Journal of Pure and Applied Algebra Volume 221, Issue 3, March 2017, Pages 499-564 (arXiv:1506.05500, doi:10.1016/j.jpaa.2016.07.003)

Related entries

• simplicial model for weak omega-categories

• stratified simplicial set

• complicial set

• Verity on descent for strict omega-groupoid valued presheaves

• infinity-cosmos

category: people