Librería Portfolio

Important growing area of mathematics
Clear definitions of all basic concepts
Combines rigour with an appealing informality
Contains precise statements of all essential theorems, with full proofs of all theorems, propositions and lemmas
Based on courses given at Carnegie Mellon University
Numerous exercises provided
New to this Edition:
Nearly a hundred new exercises
Many more examples and diagrams
Worked solutions to almost half the exercises
New coverage of monoidal categories



Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership.

Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda´s lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!

This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.



Table of Contents
Preface
1: Categories
2: Abstract Structures
3: Duality
4: Groups and Categories
5: Limits and Colimits
6: Exponentials
7: Naturality
8: Categories of Diagrams
9: Adjoints
10: Monads and Algrebras
References
Solutions to Selected Exercises
Index