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Fibered Category Morphism


Let F and G be fibered categories over a topological space X. A morphism phi:F->G of fibered categories consists of:

1. a functor phi(U):F->G(U) for each open subset U subset= X and

2. a natural isomorphism alpha_i:phi_Vi^*->i^*phi_U for each inclusion i:V↪U.

FiberedCategoryMorphismDiagram

It is required that these structures satisfy a compatibility condition with respect to the tau's, namely, that for the inclusions j:W↪V, i:V↪U, the above diagram should commute.


See also

Category, Commutative Diagram, Composition, Fibered Category, 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/abs/math/0212266.

Cite this as:

Stover, Christopher. "Fibered Category Morphism." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FiberedCategoryMorphism.html

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