• Corpus ID: 244714486

# Limits and colimits in internal higher category theory

@inproceedings{Martini2021LimitsAC,
title={Limits and colimits in internal higher category theory},
author={Louis Martini and Sebastian Johannes Wolf},
year={2021}
}
• Published 29 November 2021
• Mathematics, Philosophy
We develop a number of basic concepts in the theory of categories internal to an $\infty$-topos. We discuss adjunctions, limits and colimits as well as Kan extensions for internal categories, and we use these results to prove the universal property of internal presheaf categories. We furthermore construct the free cocompletion of an internal category by colimits that are indexed by an arbitrary class of diagram shapes.
4 Citations
Cocartesian fibrations and straightening internal to an $\infty$-topos
We define and study cartesian and cocartesian fibrations between categories internal to an ∞-topos and prove a straightening equivalence in this context.
Internal sums for synthetic fibered (∞,1)-categories
. We give structural results about biﬁbrations of (internal) ( ∞ , 1) categories with internal sums. This includes a higher version of Moens’ Theo- rem, characterizing cartesian biﬁbrations with
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