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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_functor_associative.svg?width=300.
- Monoidal_functor wikiPageID "4278182".
- Monoidal_functor wikiPageLength "5387".
- Monoidal_functor wikiPageOutDegree "16".
- Monoidal_functor wikiPageRevisionID "677791550".
- Monoidal_functor wikiPageWikiLink Braided_monoidal_categories.
- Monoidal_functor wikiPageWikiLink Braided_monoidal_category.
- Monoidal_functor wikiPageWikiLink Category:Monoidal_categories.
- Monoidal_functor wikiPageWikiLink Category_theory.
- Monoidal_functor wikiPageWikiLink Cobordism.
- Monoidal_functor wikiPageWikiLink Functor.
- Monoidal_functor wikiPageWikiLink Monoidal_adjunction.
- Monoidal_functor wikiPageWikiLink Monoidal_category.
- Monoidal_functor wikiPageWikiLink Monoidal_natural_transformation.
- Monoidal_functor wikiPageWikiLink Natural_transformation.
- Monoidal_functor wikiPageWikiLink Symmetric_monoidal_categories.
- Monoidal_functor wikiPageWikiLink Symmetric_monoidal_category.
- Monoidal_functor wikiPageWikiLink Topological_quantum_field_theory.
- Monoidal_functor wikiPageWikiLink File:Lax_monoidal_functor_associative.svg.
- Monoidal_functor wikiPageWikiLink File:Lax_monoidal_functor_braided.svg.
- Monoidal_functor wikiPageWikiLink File:Lax_monoidal_functor_left_unit.svg.
- Monoidal_functor wikiPageWikiLink File:Lax_monoidal_functor_right_unit.svg.
- Monoidal_functor wikiPageWikiLinkText "Monoidal functor".
- Monoidal_functor wikiPageWikiLinkText "monoidal functor".
- Monoidal_functor hasPhotoCollection Monoidal_functor.
- Monoidal_functor wikiPageUsesTemplate Template:Functors.
- Monoidal_functor subject Category:Monoidal_categories.
- Monoidal_functor hypernym Functors.
- 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 sameAs m.0btshn.
- Monoidal_functor sameAs Моноидальный_функтор.
- Monoidal_functor sameAs Q6901642.
- Monoidal_functor sameAs Q6901642.
- Monoidal_functor wasDerivedFrom Monoidal_functor?oldid=677791550.
- Monoidal_functor depiction Lax_monoidal_functor_associative.svg.
- Monoidal_functor isPrimaryTopicOf Monoidal_functor.