# additive functor

__мат.__аддитивный функтор

*English-Russian scientific dictionary.
2008.*

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**Additive category**— In mathematics, specifically in category theory, an additive category is a preadditive category C such that any finitely many objects A 1,..., A n of C have a biproduct A 1 ⊕ ⋯ ⊕ A n in C. (Recall that a category C is preadditive if all its… … 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**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**Additive group**— In mathematics, an additive group may be*an abelian group, when it is written using the symbol + for its binary operation *the underlying group under addition of a field, ring, vector space or other structure having addition as one of its… … 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**Derived functor**— In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. Contents 1 Motivation 2 Construction… … 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**Forgetful functor**— In mathematics, in the area of category theory, a forgetful functor is a type of functor. The nomenclature is suggestive of such a functor s behaviour: given some object with structure as input, some or all of the object s structure or properties … 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**Delta-functor**— In homological algebra, a δ functor between two abelian categories A and B is a collection of functors from A to B together with a collection of morphisms that satisfy properties generalising those of derived functors. A universal δ functor is 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

### Книги

- Categories for the Working Mathematician, Saunders Mac Lane, An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It… Категория: Научная литература Подробнее Купить за 9752 руб
- Categorical Ideas As Expressed in the Programming Language Charity. Algebras and Coalgebras, Anseok Joo, Within the past ten years, category theory has become an import avenue of research in computer science. This book explores some categorical ideas introduced by B. Jacobs and J. Rutten in "A… Категория: Книги, которые не отнесены ни к одному разделу Серия: - Издатель: Книга по Требованию, Подробнее Купить за руб