pullback property

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• Pullback (category theory) — In category theory, a branch of mathematics, a pullback (also called a fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain. The pullback is often written: P = X …   Wikipedia

• Pullback bundle — In mathematics, a pullback bundle or induced bundle is a useful construction in the theory of fiber bundles. Given a fiber bundle pi; : E rarr; B and a continuous map f : B prime; rarr; B one can define a pullback of E by f as a bundle f * E over …   Wikipedia

• Universal property — In various branches of mathematics, certain constructions are frequently defined or characterised by an abstract property which requires the existence of a unique morphism under certain conditions. These properties are called universal properties …   Wikipedia

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• Differential form — In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a better[further explanation needed] definition… …   Wikipedia

• Topos — For topoi in literary theory, see Literary topos. For topoi in rhetorical invention, see Inventio. In mathematics, a topos (plural topoi or toposes ) is a type of category that behaves like the category of sheaves of sets on a topological space.… …   Wikipedia

• Riemannian manifold — In Riemannian geometry, a Riemannian manifold ( M , g ) (with Riemannian metric g ) is a real differentiable manifold M in which each tangent space is equipped with an inner product g in a manner which varies smoothly from point to point. The… …   Wikipedia

• Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… …   Wikipedia

• Economic Affairs — ▪ 2006 Introduction In 2005 rising U.S. deficits, tight monetary policies, and higher oil prices triggered by hurricane damage in the Gulf of Mexico were moderating influences on the world economy and on U.S. stock markets, but some other… …   Universalium

• Grothendieck topology — In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a …   Wikipedia

• Direct product of groups — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia