Presheaf of Categories
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 
.
In addition, for every diagram
of topological spaces 
, 
, 
, 
, and 
, commutativity is required in the above diagram.
REFERENCES:
Brylinski, J. Loop Spaces, Characteristic Classes and Geometric Quantization. Boston: Birkhäuser, 1993.
