category of vector bundles

См. также в других словарях:

• Vector bundle — The Möbius strip is a line bundle over the 1 sphere S1. Locally around every point in S1, it looks like U × R, but the total bundle is different from S1 × R (which is a cylinder instead). In mathematics, a vector bundle is a… …   Wikipedia

• Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

• Fibred category — Fibred 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 …   Wikipedia

• Category (mathematics) — In mathematics, a category is an algebraic structure that comprises objects that are linked by arrows . A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A …   Wikipedia

• Descent (category theory) — In mathematics, the idea of descent has come to stand for a very general idea, extending the intuitive idea of gluing in topology. Since the topologists glue is actually the use of equivalence relations on topological spaces, the theory starts… …   Wikipedia

• Abelian category — In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototype example of an abelian category is the category of… …   Wikipedia

• Functor — For functors as a synonym of function objects in computer programming to pass function pointers along with its state, see function object. For the use of the functor morphism presented here in functional programming see also the fmap function of… …   Wikipedia

• Grothendieck group — In mathematics, the Grothendieck group construction in abstract algebra constructs an abelian group from a commutative monoid in the best possible way. It takes its name from the more general construction in category theory, introduced by… …   Wikipedia

• Module (mathematics) — For other uses, see Module (disambiguation). In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, wherein the corresponding scalars are allowed to lie in an arbitrary ring. Modules also… …   Wikipedia

• Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… …   Wikipedia

• Supermanifold — In physics and mathematics, supermanifolds are generalizations of the manifold concept based on ideas coming from supersymmetry. Several definitions are in use, some of which are described below. Physics In physics, a supermanifold is a manifold… …   Wikipedia