![]() 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 characterized 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. The book 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. ![]() Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. ![]()
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