associated morphism

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• 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

• *-autonomous category — In mathematics, a * autonomous (read star autonomous ) category C is a symmetric monoidal closed category equipped with a dualizing object . Contents 1 Definition 2 Properties 3 Examples …   Wikipedia

• Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… …   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

• 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

• 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

• Homological algebra — is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract… …   Wikipedia

• Group action — This article is about the mathematical concept. For the sociology term, see group action (sociology). Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle acts on the set of vertices of the… …   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

• Allegory (category theory) — In mathematics, in the subject of category theory, an allegory is a category that has some of the structure of the category of sets and binary relations between them. Allegories can be used as an abstraction of categories of relations, and in… …   Wikipedia

• Yoneda lemma — In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type morphisms into a fixed object . It is a vast generalisation of Cayley s theorem from group theory (a group being a particular kind of… …   Wikipedia