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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
Mitchell's embedding theorem — Mitchell s embedding theorem, also known as the Freyd–Mitchell theorem, is a result stating that every abelian category admits a full and exact embedding into the category of R modules. This allows one to use element wise diagram chasing proofs… … Wikipedia
Functor category — In category theory, a branch of mathematics, the functors between two given categories can themselves be turned into a category; the morphisms in this functor category are natural transformations between functors. Functor categories are of… … 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
Continuation-passing style — In functional programming, continuation passing style (CPS) is a style of programming in which control is passed explicitly in the form of a continuation. Gerald Jay Sussman and Guy L. Steele, Jr. coined the phrase in AI Memo 349 (1975), which… … Wikipedia
Algebraic geometry — This Togliatti surface is an algebraic surface of degree five. Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It… … Wikipedia
Concrete category — In mathematics, a concrete category is a category that is equipped with a faithful functor to the category of sets. This functor makes it possible to think of the objects of the category as sets with additional structure, and of its morphisms as… … Wikipedia
Groupoid — dablink|This article is about groupoids in category theory. For the algebraic structure with a single binary operation see magma (algebra). In mathematics, especially in category theory and homotopy theory, a groupoid is a simultaneous… … Wikipedia
Inaccessible cardinal — In set theory, an uncountable regular cardinal number is called weakly inaccessible if it is a weak limit cardinal, and strongly inaccessible, or just inaccessible, if it is a strong limit cardinal. Some authors do not require weakly and strongly … Wikipedia
Presheaf (category theory) — In category theory, a branch of mathematics, a V valued presheaf F on a category C is a functor F:C^mathrm{op} omathbf{V}. Often presheaf is defined to be a Set valued presheaf. If C is the poset of open sets in a topological space, interpreted… … Wikipedia
