Categories for the Working Mathematician (Graduate Texts in Mathematics)
| Author | : | |
| Rating | : | 4.82 (760 Votes) |
| Asin | : | 0387984038 |
| Format Type | : | paperback |
| Number of Pages | : | 317 Pages |
| Publish Date | : | 2017-04-23 |
| Language | : | English |
DESCRIPTION:
"A Classic" according to Jason Schorn. Well, let us think about this a little bitYou want to learn Category theory, whether for some course or just for the fun of it, and now where do you turn in order to learn the necessary concepts. If you are a mathematician and have some experience, then you turn to the masters, the originators of the given subject and read their work. Sure, being the founder of a given subject does not imply that you are a good exposi. Simply Great Have you ever tried reading Descartes' "Geometry"? It's not a good place to learn about coordinate geometry. I tried. This was almost 10 years ago, but I still remember it pretty well. Ok, so maybe the experience was even a bit traumatic. Usually when someone works out a theory, it takes a fresh perspective (or two, or you get it) to really digest it, and come up with a reasonable way of teaching it to newcomers. It'. "One of the great books in mathematics" according to Colin McLarty. This book is a classic. Clearly written, drawing on a vast number of different applications and motivations for the subject. Eilenberg and Mac Lane created category theory and this book is alive with the very style of thought Mac Lane brought to it in the first place. It is obvious that Mac Lane wrote each page, and each exercise, with a view of the whole book in mind. He starts with the very basics, assuming indeed t
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. 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. An array of general ideas useful in a wide variety of fields
… the book remains an authoritative source on the foundations of the theory and an accessible first introduction to categories. LaneCategories for the Working Mathematician"A very useful introduction to category theory."INTERNATIONALE MATHEMATISCHE NACHRICHTEN. … It is very well-written, with plenty of interesting discussions and stimulating exercises.” (Ittay Weiss, MAA Reviews, July, 2014)Second EditionS.M. From the reviews of the second edition:“The book under review is an introduction to the theory of categories which, as the title suggests, is addressed to the (no-nonsense) working mathematician, thus presenting the ideas and concepts of Category Theory in a broad context of mainstream examples (primarily from algebra)