Titlebook: Categories for the Working Mathematician; Saunders Mac Lane Textbook 1978Latest edition Springer Science+Business Media New York 1978 Adjo

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Textbook 1978Latest editionmber of revisions and additions, including two new chapters on topics of active interest. One is onsymmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into

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0072-5285 monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into 978-1-4419-3123-8978-1-4757-4721-8Series ISSN 0072-5285 Series E-ISSN 2197-5612

COLON

Introduction, of arrows. Each arrow . : . → . represents a function; that is, a set ., a set ., and a rule . ? . which assigns to each element . ∈ . an element . ∈ .; whenever possible we write . and not .(.), omitting unnecessary parentheses.

interference

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BURSA

Monads and Algebras,the category .. of all algebras of the given type, the forgetful functor .: ..→., and its left adjoint ., which assigns to each set . the free algebra . of type τ generated by elements of .. . trace of this adjunction 〈.,.,.〉: . ?.. resides in the category .; indeed, the composite . = . is a functor

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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

Nomogram

Abelian Categories,e abelian groups and composition is bilinear), all finite limits and colimits exist, and these limits — especially kernel and cokernel — are well behaved. This leads to a set of axioms describing an “abelian” category. The axioms suffice to prove all the facts about commuting diagrams and connecting

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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 when

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