Titlebook: Categories for the Working Mathematician; Saunders Mac Lane Textbook 19711st edition Springer Science+Business Media New York 1971 Adjoint

Morsel

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 <., ., ?>: . ? . resides in the category .; indeed, the composite .=. is a functor . → .,

晚間

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

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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

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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

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