ОАО Киномаза

Автор: katya | 3rd Октябрь, 2016

Every fan of World of Tanks should know that it is possible now to find and buy the different items based on this game. The merchandise for any taste is available at our website https://jagfox.com/product-category/world-of-tanks

In the mathematical field of category theory, the product of two categories C and D, denoted C × D and called a product category, is a straightforward extension of the concept of the Cartesian product of two sets.
The product category C × D has:

as objects:
pairs of objects (A, B), where A is an object of C and B of D;
as arrows from (A1, B1) to (A2, B2):
pairs of arrows (f, g), where f : A1 → A2 is an arrow of C and g : B1 → B2 is an arrow of D;
as composition, component-wise composition from the contributing categories:
(f2, g2) o (f1, g1) = (f2 o f1, g2 o g1);
as identities, pairs of identities from the contributing categories:
1(A, B) = (1A, 1B).
For small categories, this is the same as the action on objects of the categorical product in the category Cat. A functor whose domain is a product category is known as a bifunctor. An important example is the Hom functor, which has the product of the opposite of some category with the original category as domain:

Hom : Cop × C → Set.
Just as the binary Cartesian product is readily generalized to an n-ary Cartesian product, binary product of two categories can be generalized, completely analogously, to a product of n categories. The product operation on categories is commutative and associative, up to isomorphism, and so this generalization brings nothing new from a theoretical point of view.
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