Functor category
Functor category In category theory, a branch of mathematics, the functors ... categories can themselves be turned into a category; the morphisms in this functor category are natural transformations between functors. ...
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Functor
Functor For functors in computer science, see the function object article. In category theory, a functor is a special type of mapping between ... be thought of as morphisms in the category of small categories. Functors were first considered ... Let C and D be categories. A functor F from C to D is ...
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Functor   (translated from French)
Functor theory of the categories The concept of functor is during categorical concept ofapplication for ensembles . Definitions One functor covariant of one category \mathcal C in a \mathcal category It , is a rule, note ...
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Category theory
Category theory In mathematics, category theory deals in an abstract way with ... connection with algebraic topology. See list of category theory topics for a breakdown of relevant ... structure, as mathematical theories have traditionally done, category theory emphasizes the morphisms — the structure ... investigation occurs in many mathematical theories. A category is an axiomatic formulation of this ...
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Comma category
Comma category A comma category (also sometimes called a slice category) is a construction in category theory, a branch of mathematics. It provides ... instead of simply relating objects of a category to one another, they become objects ...
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Category theory   (translated from Chinese)
Category theory Sees alsoCategory Category theoryAbstractly processes which between the mathematical framework ... call it "the generalized abstract nonsense"The category discusses appears in the very most study ... mathematics objects (for instance group) itself, the category discusses makes the principle is needs to ... mapping is so-calledGroup homomorphism. The different category may useFunctorRelates. The functor was has ...
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Derived functor
Derived functor In mathematics, certain functors may be derived ... we are given a covariant left exact functor F : A → B between two abelian ... F. For every i≥1, there is a functor R i F: A → B, and ... we see that F is an exact functor if and only if R 1 F ... injective, then the sequence splits. Applying a functor to a split sequence results in ...
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Representable functor
Representable functor In mathematics, especially in category theory, a representable functor is a functor of a special form from an arbitrary category into the category of sets. Such ...
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Limit (category theory)
Limit (category theory) In category theory, a branch of mathematics, the abstract ... auxiliary notion of a cone of a functor. Cones are also perhaps more aptly called ... categories J and C and a covariant functor F : J → C. In this situation ... the apex L. A limit of a functor is just a universal cone. In ...
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Forgetful functor
Forgetful functor A forgetful functor is a type of functor in mathematics. The nomenclature is suggestive of such a functor's behaviour: given some object with structure ... is left as an empty list , the functor is simply to take the underlying ...
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