finitely cocomplete category

A **finitely cocomplete category** is a category $C$ which admits all *finite* colimits, that is a colimit for any finite diagram $F: J \to C$. Finitely cocomplete categories are also called **rex categories**, although this is rarer than ‘lex’ for finitely complete categories. Compare a cocomplete category, which has all small colimits.

For further theory, see finitely complete category. Note that $C$ is finitely cocomplete if and only if its opposite category $C^op$ is finitely complete.

Last revised on May 30, 2009 at 16:46:21. See the history of this page for a list of all contributions to it.