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

By Saunders Mac Lane

An array of basic principles worthwhile in a large choice of fields. ranging from the principles, this e-book illuminates the strategies of type, functor, traditional 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 broadly illustrated within the ultimate chapters, which come with many functions of the elemental life theorem for adjoint functors. the types of algebraic platforms are produced from definite adjoint-like facts and characterized by way of Beck's theorem. After contemplating a number of purposes, the publication keeps with the development and exploitation of Kan extensions. This moment variation incorporates a variety of revisions and additions, together with new chapters on themes of lively 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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