product functor
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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
Product (category theory) — In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct… … 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
Product category — In the mathematical field of category theory, the product of two categories C and D , denoted nowrap| C × D and called a product category, is a straightforward extension of the concept of the Cartesian product of two sets.DefinitionThe product… … Wikipedia
Diagonal functor — In category theory, for any object a in any category where the product exists, there exists the diagonal morphism satisfying for , where πk … Wikipedia
Hom functor — In mathematics, specifically in category theory, Hom sets, i.e. sets of morphisms between objects, give rise to important functors to the category of sets. These functors are called Hom functors and have numerous applications in category theory… … Wikipedia
Tor functor — In higher mathematics, the Tor functors of homological algebra are the derived functors of the tensor product functor. They were first defined in generality to express the Künneth theorem and universal coefficient theorem in algebraic… … Wikipedia
Predicate functor logic — In mathematical logic, predicate functor logic (PFL) is one of several ways to express first order logic (formerly known as predicate logic) by purely algebraic means, i.e., without quantified variables. PFL employs a small number of algebraic… … Wikipedia
Smash product — In mathematics, the smash product of two pointed spaces (i.e. topological spaces with distinguished basepoints) X and Y is the quotient of the product space X times; Y under the identifications ( x , y 0) sim; ( x 0, y ) for all x isin; X and y… … Wikipedia
Tensor product of modules — In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (roughly speaking, multiplication ) to be carried out in terms of linear maps (module homomorphisms). The module construction is analogous… … Wikipedia
Exact functor — In homological algebra, an exact functor is a functor, from some category to another, which preserves exact sequences. Exact functors are very convenient in algebraic calculations, roughly speaking because they can be applied to presentations of… … Wikipedia
