On 2-categorical infinity-cosmoi

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Authors	BOURKE John Denis LACK Stephen
Year of publication	2024
Type	Article in Periodical
Magazine / Source	Journal of Pure and Applied Algebra
MU Faculty or unit	Faculty of Science
Citation
Web	https://www.sciencedirect.com/science/article/pii/S0022404924000586
Doi	http://dx.doi.org/10.1016/j.jpaa.2024.107661
Keywords	infinity-categories; accessible and locally presentable categories; Enriched categories; Homotopical algebra
Description	Recently Riehl and Verity have introduced infinity-cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those infinity-cosmoi which are in fact 2-categories; we shall refer to these as 2-cosmoi. We show that each 2-category with flexible limits gives rise to a 2-cosmos whose distinguished class of isofibrations consists of the normal isofibrations. Many examples arise in this way, and we show that such 2-cosmoi are minimal as Cauchycomplete 2-cosmoi. Finally, we investigate accessible 2-cosmoi and develop a few aspects of their basic theory.
Related projects:	Enriched categories and their applications