Colimit criterion for representability of a presheaf
= Colimit criterion for representability of a presheaf
A <categorical presheaf> is <representable> if its elements projection has a <colimit> and the presheaf preserves the opposite-indexed <categorical limit> of that projection. Compatibility of all distinguished elements then supplies a <universal element> at the colimit object. The preservation requirement must cover this diagram even when its indexing <category> is large.