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fibered
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Definitions of fibered in various dictionaries:
adj - a thread or threadlike object or structure [n -S] : FIBERED
FIBERED - Fibred categories (or fibered categories) are abstract entities in mathematics used to provide a general framework for descent theory. They formalise...
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Having fibers fibres |
Medical bDefinitionb of bFIBERb. 1. : a thread or a threadlike structure or object: as a : a strand of nerve tissue : axon, dendrite b : one of the filaments composing most of the intercellular matrix of connective tissue c : one of the elongated contractile cells of muscle tissue. |
Fibered description |
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Fibred categories (or fibered categories) are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the various situations in geometry and algebra in which inverse images (or pull-backs) of objects such as vector bundles can be defined. As an example, for each topological space there is the category of vector bundles on the space, and for every continuous map from a topological space X to another topological space Y is associated the pullback functor taking bundles on Y to bundles on X. Fibred categories formalise the system consisting of these categories and inverse image functors. Similar setups appear in various guises in mathematics, in particular in algebraic geometry, which is the context in which fibred categories originally appeared. Fibered categories are used to define stacks, which are fibered categories (over a site) with "descent". Fibrations also play an important role in categorical semantics of type theory, and in particular that of dependent type theories. * Fibred categories were introduced by Alexander Grothendieck (1959, 1971), and developed in more detail by Jean Giraud (1964, 1971). |