issues to appear, and it is this set-up that fibred categories formalise. The main application of fibred categories is in descent theory, concerned with a vast...
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Stack (mathematics) (redirect from Stack (category theory))
formally given as a fibred category over another base category, where the base has a Grothendieck topology and where the fibred category satisfies a few axioms...
34 KB (5,113 words) - 13:10, 4 October 2024
Pullback (section Generalizations and category theory)
algebraic topology and differential geometry. See also: Pullback (category theory) Fibred category Inverse image sheaf When the pullback is studied as an operator...
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Grothendieck construction (category Category theory)
mathematical field of category theory. It is a fundamental construction in the theory of descent, in the theory of stacks, and in fibred category theory. In categorical...
5 KB (964 words) - 20:17, 7 February 2024
functor of the third kind is the functor Mod → Ab, where Mod is the fibred category of all modules over arbitrary rings. To see this, just choose a ring...
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categories. Any indexed category has an associated Grothendieck construction, which gives rise to a fibred category. Indexed category at the nLab v t e...
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consider the category of families on B with only isomorphisms between families taken as morphisms. One then considers the fibred category which assigns...
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of a fibration generalizes the notion of a fiber bundle and plays an important role in algebraic topology, a branch of mathematics. Fibrations are used...
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was made interim director in 1994 and director from 1995 to 2000. Fibred category "Giraud, Jean (1936–2007)". BnF catalogue général. Bibliothèque nationale...
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{\displaystyle {\text{Cat}}} is the 2-category of small categories. Another way to view this is as a fibred category [ U / R ] → ( S c h / S ) {\displaystyle...
24 KB (3,767 words) - 18:36, 1 October 2024