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- Monoidal_functor abstract "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 The coherence maps of lax monoidal functors satisfy no additional properties; they are not necessarily invertible. The coherence maps of strong monoidal functors are invertible. The coherence maps of strict monoidal functors are identity maps.Although we distinguish between these different definitions here, authors may call any one of these simply monoidal functors.".
- Monoidal_functor thumbnail Lax_monoidal_funct_assoc.png?width=300.
- Monoidal_functor wikiPageID "4278182".
- Monoidal_functor wikiPageRevisionID "585204569".
- Monoidal_functor hasPhotoCollection Monoidal_functor.
- Monoidal_functor subject Category:Monoidal_categories.
- Monoidal_functor type Abstraction100002137.
- Monoidal_functor type Class107997703.
- Monoidal_functor type Collection107951464.
- Monoidal_functor type Group100031264.
- Monoidal_functor type MonoidalCategories.
- Monoidal_functor comment "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.".
- Monoidal_functor label "Monoidal functor".
- Monoidal_functor label "Моноидальный функтор".
- Monoidal_functor sameAs m.0btshn.
- Monoidal_functor sameAs Q6901642.
- Monoidal_functor sameAs Q6901642.
- Monoidal_functor sameAs Monoidal_functor.
- Monoidal_functor wasDerivedFrom Monoidal_functor?oldid=585204569.
- Monoidal_functor depiction Lax_monoidal_funct_assoc.png.
- Monoidal_functor isPrimaryTopicOf Monoidal_functor.