nLab finitely cocomplete category



Category theory

Limits and colimits



A finitely cocomplete category is a category π’ž\mathcal{C} which admits all finite colimits, that is a colimit for any finite diagram F:π’₯β†’π’žF \colon \mathcal{J} \to \mathcal{C}.

(A category with all small colimit is called a cocomplete category).

This is the notion formally dual to that of finitely complete categories, see there for more.

Finitely cocomplete categories are also called rex categories, although this is rarer than β€˜lex’ for finitely complete categories.

Last revised on February 17, 2024 at 09:20:35. See the history of this page for a list of all contributions to it.