A presheaf 
of categories consists of the following data:
1. For every local homeomorphism 
of topological
spaces 
,
,
a category 
;
2. For every diagram 
of local homeomorphisms, a functor 
;
3. For every diagram 
of local homeomorphisms, an invertible natural transformation 
.
Use the normalized identity convention: the restriction functor associated with an identity map is the identity functor, and 
and 
are identity natural
transformations.
In addition, for every diagram
 |
of topological spaces 
, 
, 
, 
, and 
, commutativity is required in the above diagram.
