Conceptual Mathematics
A First Introduction to Categories

This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

F. William Lawvere (Author), Stephen H. Schanuel (Author)

9780521719162, Cambridge University Press

Paperback, published 30 July 2009

404 pages, 575 b/w illus. 12 tables 213 exercises
24.4 x 17.1 x 2.5 cm, 0.78 kg

'Conceptual Mathematics is the first book to serve both as a skeleton key to mathematics for the general reader or beginning student and as an introduction to categories for computer scientists, logicians, physicists, linguists, etc … The fundamental ideas are illuminated in an engaging way.' L'Enseignment Mathématique

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.

Foreword
Note to the reader
Preview
Part I. The Category of Sets: 1. Sets, maps, composition
Part II. The Algebra of Composition: 2. Isomorphisms
Part III. Categories of Structured Sets: 3. Examples of categories
Part IV. Elementary Universal Mapping Properties: 4. Universal mapping properties
Part V. Higher Universal Mapping Properties: 5. Map objects
6. The contravariant parts functor
7. The components functor
Appendix 1. Geometry of figures and algebra of functions
Appendix 2. Adjoint functors
Appendix 3. The emergence of category theory within mathematics
Appendix 4. Annotated bibliography.

Subject Areas: Algebra [PBF], Mathematical logic [PBCD]