# nLab ideal completion

The ideal completion of a category $C$ generalises the notion of ideal completion of a partially ordered set. It is formed by taking the category of ideals? of $C$. It is the completion of $C$ under filtered colimits of monomorphisms.

See page 24 of An Outline of Algebraic Set Theory.

“The actual definition requires either some care in specifying choices of monomorphisms, as is done in 4, or a sheaf-theoretic approach as in 5.”

Revised on June 9, 2011 07:36:22 by Andrew Stacey (129.241.15.200)