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.
See also
Category,
Category Theory,
Commutative Diagram,
Functor,
Homeomorphism,
Presheaf,
Sheaf,
Topological Space
This entry contributed by Christopher
Stover
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References
Brylinski, J. Loop Spaces, Characteristic Classes and Geometric Quantization. Boston: Birkhäuser,
1993.
Cite this as:
Stover, Christopher. "Presheaf of Categories." From MathWorld--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/PresheafofCategories.html
Subject classifications
