Morsel
发表于 2025-3-26 21:10:10
Monads and Algebras,egory . of all algebras of the given type, the forgetful functor .: . →., and its left adjoint ., which assigns to each set . the free algebra . of type . generated by elements of .. A trace of this adjunction <., ., ϕ>: . ⇀ . resides in the category .; indeed, the composite .=. is a functor . → .,
晚间
发表于 2025-3-27 02:52:10
Monoids,d by the usual diagrams relative to the cartesian product × in ., while a ring is a monoid in ., relative to the tensor product ⊗ there. Thus we shall begin with categories . equipped with a suitable bifunctor such as × or ⊗, more generally denoted by □. These categories will themselves be called “m
Canary
发表于 2025-3-27 07:31:31
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Override
发表于 2025-3-27 11:59:25
Kan Extensions, defining such an extension. However, if . is a subcategory of ., each functor .:. → . has in principle . canonical (or extreme) “extensions” from . to functors ., .: . → .. These extensions are characterized by the universality of appropriate natural transformations; they need not always exist, but
团结
发表于 2025-3-27 15:24:37
Textbook 19711st edition in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with a
incarcerate
发表于 2025-3-27 18:10:39
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FRET
发表于 2025-3-27 23:22:03
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悬崖
发表于 2025-3-28 06:07:30
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gusher
发表于 2025-3-28 07:38:52
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我不死扛
发表于 2025-3-28 12:36:25
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