In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗ : C × C → C {\displaystyle...
17 KB (2,389 words) - 13:47, 27 June 2024
as category theory, a monoidal category where the monoidal ("tensor") product is the categorical product is called a cartesian monoidal category. Any...
5 KB (571 words) - 09:52, 5 February 2021
In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" ⊗ {\displaystyle...
5 KB (631 words) - 00:45, 10 July 2023
example is the category of sets, Set, where the monoidal product of sets A {\displaystyle A} and B {\displaystyle B} is the usual cartesian product A × B...
7 KB (1,167 words) - 18:33, 17 September 2023
monoidal category M. For the case that M is the category of sets and (⊗, I, α, λ, ρ) is the monoidal structure (×, {•}, ...) given by the cartesian product...
14 KB (1,966 words) - 18:25, 14 August 2024
category of sets (with the monoidal structure induced by the Cartesian product), is a monoid in the usual sense. A monoid object in Top, the category...
5 KB (511 words) - 14:20, 31 January 2024
In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with...
18 KB (2,587 words) - 11:15, 8 August 2024
Closed monoidal category Braided monoidal category Topos Category of small categories Semigroupoid Comma category Localization of a category Enriched...
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by the cartesian product of sets. It is also a monoidal category if one defines the monoidal product by the disjoint union of sets. The category Rel was...
7 KB (732 words) - 20:50, 19 May 2023
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...
15 KB (1,978 words) - 02:10, 30 July 2024