Refinement (category theory)

In category theory and related fields of mathematics, a refinement is a construction that generalizes the operations of "interior enrichment", like bornologification or saturation of a locally convex space.

A dual construction is called envelope.

The definition[1] of a refinement of

Notations: In a special case when

is a class of all morphisms whose ranges belong to a given class of objects

in the notations (and in the terms): Similarly, if

is a class of all morphisms whose ranges belong to a given class of objects

in the notations (and in the terms): For example, one can speak about a refinement of

by means of the class of objects