Monoidal category: Difference between revisions
(New page: {{category plus additional structure}} ==Definition== A '''monoidal category''' is a category <math>\mathcal{C}</math> equipped with an additional operation, called a monoidal operat...) |
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<math>\otimes: \operatorname{Ob}\mathcal{C} \times \operatorname{Ob}\mathcal{C} \to \operatorname{Ob}\mathcal{C}</math> | <math>\otimes: \operatorname{Ob}\mathcal{C} \times \operatorname{Ob}\mathcal{C} \to \operatorname{Ob}\mathcal{C}</math> | ||
along with, for every <math>A,B,C,D \in \operatorname{Ob}\mathcal{C}</math>, a map: | |||
<math>\otimes: \mathcal{C}(A,B) \times \mathcal{C}(C,D) \to \mathcal{C}(A \otimes C, B \otimes D)</math> | |||
satisfying the following conditions: | satisfying the following conditions: | ||
* ''' | * '''Functorial in both variables''': | ||
* '''Has an identity upto natural isomorphism''' | * '''Has an identity upto natural isomorphism''': | ||
* '''Associative upto natural isomorphism''' | * '''Associative upto natural isomorphism''': | ||
Latest revision as of 02:00, 9 December 2008
This article defines a notion of a category along with some additional structure.
View other such notions
Definition
A monoidal category is a category equipped with an additional operation, called a monoidal operation:
along with, for every , a map:
satisfying the following conditions:
- Functorial in both variables:
- Has an identity upto natural isomorphism:
- Associative upto natural isomorphism: