nLab
finitely cocomplete category

A finitely cocomplete category is a category CC which admits all finite colimits, that is a colimit for any finite diagram F:JCF: 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 CC is finitely cocomplete if and only if its opposite category C opC^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.