Colimits and cocompletions in internal higher category theory

Louis Martini; Sebastian Wolf

Colimits and cocompletions in internal higher category theory

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arxiv 2111.14495 v3 pith:2G5MPV4E submitted 2021-11-29 math.CT math.AT

Louis Martini , Sebastian Wolf This is my paper · ORCID

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keywords internalcategoriescolimitscategorytheoryadjunctionsarbitrarybasic

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abstract

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.

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Cited by 1 Pith paper

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Approximate Fibrations in Higher Topos Theory
math.GT 2025-10 accept novelty 7.0 of 10

Approximate fibrations, previously defined only for topological spaces, are reformulated for higher topoi and shown to coincide with the classical notion for proper maps of locally compact ANRs.

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