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.
On enriched category theory and internal categories:
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 (∞,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 $\infty$-Category Theory (2021) (pdf)
On (∞,1)-functors and (∞,1)-monads:
On the Yoneda lemma for (∞,1)-categories:
Last revised on October 13, 2021 at 12:05:23. See the history of this page for a list of all contributions to it.