A fibered category
over a topological space consists of
1. a category for each open subset ,
2. a functor for each inclusion , and
3. a natural isomorphism
for each pair of inclusions , .
In addition, for any three composable inclusions , , and , there exists a natural commuting
as shown above.
Sometimes, the pair
is used to denote a fibered category with more precision while the shorthand is sometimes used for , , .
See also
Category,
Commutative Diagram,
Composition,
Fibered
Category Morphism,
Functor,
Inclusion
Map,
Isomorphism,
Morphism,
Open Set,
Topological
Space
This entry contributed by Christopher
Stover
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References
Moerdijk, I. "Introduction to the Language of Stacks
and Gerbes." 2002. http://arxiv.org/pdf/math/0212266v1.pdf.
Cite this as:
Stover, Christopher. "Fibered Category." From MathWorld--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/FiberedCategory.html
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