Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
The 2-Giraud theorem is the generalization of Giraud's theorem from topos theory to 2-topos theory.
The following theorem, which generalizes the classical Giraud theorem, is due to StreetCBS.
For a 2-category , the following are equivalent.
In fact, it is not hard to prove the same theorem for n-categories, for any .
For an n-category , the following are equivalent.
- is equivalent to the -category of n-sheaves on a small n-site.
- is an infinitary n-pretopos with a small eso-generator?.
- is a reflective sub--category of a category of -presheaves with left-exact reflector.
For this is Street’s theorem; for it is the classical theorem. The other values included are of course and .
Created on March 9, 2012 18:53:53
by Urs Schreiber