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Internal sums for synthetic fibered (∞,1)-categories.

Authors :
Weinberger, Jonathan
Source :
Journal of Pure & Applied Algebra. Sep2024, Vol. 228 Issue 9, pN.PAG-N.PAG. 1p.
Publication Year :
2024

Abstract

We give structural results about bifibrations of (internal) (∞ , 1) -categories with internal sums. This includes a higher version of Moens' Theorem, characterizing cartesian bifibrations with extensive aka stable and disjoint internal sums over lex bases as Artin gluings of lex functors. We also treat a generalized version of Moens' Theorem due to Streicher which does not require the Beck–Chevalley condition. Furthermore, we show that also in this setting the Moens fibrations can be characterized via a condition due to Zawadowski. Our account overall follows Streicher's presentation of fibered category theory à la Bénabou, generalizing the results to the internal, higher-categorical case, formulated in a synthetic setting. Namely, we work inside simplicial homotopy type theory, which has been introduced by Riehl and Shulman as a logical system to reason about internal (∞ , 1) -categories, interpreted as Rezk objects in any given Grothendieck–Rezk–Lurie (∞ , 1) -topos. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00224049
Volume :
228
Issue :
9
Database :
Academic Search Index
Journal :
Journal of Pure & Applied Algebra
Publication Type :
Academic Journal
Accession number :
176810578
Full Text :
https://doi.org/10.1016/j.jpaa.2024.107659