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In category theory, monoidal functors are … 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.any one of these simply monoidal functors.
, В теории категорий моноидальные функторы — это функторы между моноидальными категориями, сохраняюющие моноидальную структуру, то есть умножение и тождественный элемент.
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| rdfs:comment |
In category theory, monoidal functors are … 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 different definition of monoidal functors
, В теории категорий моноидальные функторы — это функторы между моноидальными категориями, сохраняюющие моноидальную структуру, то есть умножение и тождественный элемент.
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| rdfs:label |
Monoidal functor
, Моноидальный функтор
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