mac lane categories for the working mathematician pdf

Symmetry and Braiding in Monoidal CategoriesĤ. Categories, Functors, and Natural Transformations 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. The book then turns to adjoint functors, which provide a description of universal. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. 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. Description: Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields.

Book Description An array of general ideas useful in a wide variety of fields. An array of general ideas useful in a wide variety of fields. Author: Saunders Mac Lane Publisher: Springer Science & Business Media ISBN: 1475747217 Category : Mathematics Languages : en Pages : 317.

Mac lane categories for the working mathematician pdf