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.

Revised on May 30, 2009 16:46:21 by Toby Bartels (71.104.230.172)