pullback diagram
1Pullback (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 …
2Pullback 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 …
3Diagram (category theory) — In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory. The primary difference is that in the categorical setting one has morphisms. An indexed family of sets is a collection of sets …
4Subobject classifier — In category theory, a subobject classifier is a special object Omega; of a category; intuitively, the subobjects of an object X correspond to the morphisms from X to Omega;. As the name suggests, what a subobject classifier does is to… …
5List of mathematics articles (P) — NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… …
6Limit (category theory) — In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint… …
7Span (category theory) — A span, in category theory, is a generalization of the notion of relation between two objects of a category. When the category has all pullbacks (and satisfies a small number of other conditions), spans can be considered as morphisms in a… …
8Regular category — In category theory, a regular category is a category with finite limits and coequalizers of kernel pairs, satisfying certain exactness conditions. In that way, regular categories recapture many properties of abelian categories, like the existence …
9Grothendieck 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 …
10Pushforward (differential) — Suppose that phi; : M → N is a smooth map between smooth manifolds; then the differential of phi; at a point x is, in some sense, the best linear approximation of phi; near x . It can be viewed as generalization of the total derivative of… …
