nLab finitely cocomplete (infinity,1)-category

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Idea

Finitely cocomplete $(\infty,1)$ -categories are the analog in (∞,1)-category theory of finitely cocomplete categories in category theory.

Let $\mathcal{C}$ be an (∞,1)-category. This is called a finitely cocomplete $(\infty,1)$ -category if $\mathcal{C}$ has finite (∞,1)-colimits, i.e.

if it has an initial object and (∞,1)-pushouts;
if it has an initial object and for every object $x \in C$ , the under-(∞,1)-category $C_{/x}$ has finite coproducts.

Created on April 10, 2025 at 05:33:41. See the history of this page for a list of all contributions to it.