![]() ![]() This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. ![]() ![]() PDF ML for the Working Programmer, 2nd Edition. PDF Set Theory for the Working Mathematician (London Mathematical Society Student Texts) PDF Nonstandard Analysis for the Working Mathematician - Removed. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. Saunders Mac Lane - Categories for the Working Mathematician. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. An array of general ideas useful in a wide variety of fields. ![]()
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