neighborhood of a topologizing subcategory
Given a topologizing subcategory of an abelian category , the -th neighborhood of is the -th power of with respect to the Gabriel multiplication of topologizing subcategories.
The union is a topologizing subcategory of closed under extensions (that is a thick subcategory in the strong sense).
A typical example is when is the minimal “subscheme” (= coreflective topologizing subcategory) of the category of additive endofunctors containing the identity functor. See differential monad.
Revised on May 5, 2011 15:44:34
by Zoran Škoda