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About: Monoidal functor     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatMonoidalCategoriesyago:Abstraction100002137yago:Class107997703yago:Collection107951464yago:Group100031264 New Facet based on Instances of this Class

In category theory, monoidal functors are functors between monoidal categories which preserve the monoidal structure. More specifically, a monoidal functor between two monoidal categories consists of a functor between the categories, along with two coherence maps—a natural transformation and a morphism that preserve monoidal multiplication and unit, respectively. Mathematicians require these coherence maps to satisfy additional properties depending on how strictly they want to preserve the monoidal structure; each of these properties gives rise to a slightly different definition of monoidal functors