category of open subsets
Cohomology and homotopy
In higher category theory
Category of open subsets
Given a topological space , the category of open subsets of is the category whose
The category is a poset, in fact a frame (dually a locale): it is the frame of opens of .
The category is naturally equipped with the structure of a site, where a collection of morphisms is a cover precisely if their union in equals :
\bigcup_i U_i = U .
The category of sheaves on equipped with this site structure is usually written
Sh(X) := Sh(Op(X))
Revised on August 31, 2012 14:27:37
by Urs Schreiber