Categories for the Working Mathematician (Graduate Texts in by Saunders Mac Lane

By Saunders Mac Lane

An array of basic principles beneficial in a large choice of fields. ranging from the principles, this ebook illuminates the recommendations of class, functor, typical transformation, and duality. It then turns to adjoint functors, which supply an outline of common buildings, an research of the representations of functors by means of units of morphisms, and a way of manipulating direct and inverse limits. those specific innovations are generally illustrated within the final chapters, which come with many purposes of the elemental lifestyles theorem for adjoint functors. the types of algebraic platforms are created from sure adjoint-like facts and characterized via Beck's theorem. After contemplating a number of functions, the booklet keeps with the development and exploitation of Kan extensions. This moment variation features a variety of revisions and additions, together with new chapters on subject matters of energetic curiosity: symmetric monoidal different types and braided monoidal different types, and the coherence theorems for them, in addition to 2-categories and the better dimensional different types that have lately come into prominence.

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