Product Description

Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. 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. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.

Product Details

• Amazon Sales Rank: #304015 in Books
• Published on: 1998-10-01
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 314 pages

Customer Reviews

Really, totally enjoyable
I realized that this book was a real treasure when I misplaced it for a year or two (finally it turned up in a packing case in the roof) and I had to sift through a lot of text in other books (Joshi, for instance). Good grief. This book introduces the subject in such a straightfoward way it is really hard to miss the point. His chapter on Monoidal categories, for instance, is really brilliant! I so much prefer MacLanes approach than that taken by many others, seeing it as an extension of homology theory, which makes it so hard for computer scientists to get into it...

Its a wee bit expensive, but very hard to put down, I really and truly recommend it...

Old but gold
Obviously pre-dates all the recent important work on applications of cat theory in comp sci, but remains one of the most solid grounding in the basic concepts - cetainly well ahead of the course where I first studied the subject, and a useful reference all the way up to PhD level