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monoidal category

(Definition)

A monoidal category is a category which has the structure of a monoid, that is, among the objects there is a binary operation which is associative and has an unique neutral element.

A prototype is the category of isomorphism classes of vector spaces over a field $\mathbb{K}$ , herein the tensor product is the associative operation and the same field $\mathbb{K}$ is the neutral element.

Monoidal categories play an important role in the topological quantum field theories.

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"monoidal category" is owned by juanman. [ full author list (2) ]

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Other names:

monoid

Keywords:

Category, monoidal category, algebroids, topological quantum field theories, TQFT, monoidal category

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Cross-references: quantum field theories, operation, tensor product, field, vector spaces, classes, isomorphism, neutral element, associative, binary operation, objects, structure, category
There are 24 references to this entry.

This is version 6 of monoidal category, born on 2006-12-24, modified 2008-08-20.
Object id is 8681, canonical name is MonoidalCategory.
Accessed 829 times total.

Classification:

AMS MSC:	18D10 (Category theory; homological algebra :: Categories with structure :: Monoidal categories , symmetric monoidal categories, braided categories)
	18-00 (Category theory; homological algebra :: General reference works )
	81-00 (Quantum theory :: General reference works )

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