On 2-categorical ∞-cosmoi

John Bourke; Stephen Lack

doi:10.1016/j.jpaa.2024.107661

On 2-categorical ∞-cosmoi

John Bourke, Stephen Lack^*

^*Corresponding author for this work

School of Mathematical and Physical Sciences

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Abstract

Recently Riehl and Verity have introduced ∞-cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those ∞-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 Cauchy-complete 2-cosmoi. Finally, we investigate accessible 2-cosmoi and develop a few aspects of their basic theory.

Original language	English
Article number	107661
Pages (from-to)	1-26
Number of pages	26
Journal	Journal of Pure and Applied Algebra
Volume	228
Issue number	9
DOIs	https://doi.org/10.1016/j.jpaa.2024.107661
Publication status	Published - Sept 2024

Bibliographical note

Copyright © 2024 The Authors. Published by Elsevier B.V. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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N2 - Recently Riehl and Verity have introduced ∞-cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those ∞-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 Cauchy-complete 2-cosmoi. Finally, we investigate accessible 2-cosmoi and develop a few aspects of their basic theory.

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On 2-categorical ∞-cosmoi

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