Monoidal category

Monoidal functor

Let be monoidal categories.1 A functor is called monoidal iff it is eqquipped with an isomorphism in and a natural isomorphism with components in , compatible with associativity

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and unitality

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Iff and are identities, then is called strict monoidal.2 If and are braided, then a monoidal functor is said to be braided iff

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commutes for all objects .

Examples

See also

#state/tidy | #lang/en | #SemBr

Footnotes

  1. As usual we overload and to denote the tensor products and units of both categories. ↩

  2. 1966. Closed categories, §II.1, p. 473 ↩