Arrows, Structures, and Functors: The Categorical Imperative

by Michael A. Arbib

Category theory is a mathematician's attempt to lay bare some of the underlying principles common to diverse fields in the mathematical sciences. It has become, as well, an area of pure mathematics in its own right. The contribution of our book, then, is to build up a sufficient perspective without demanding more of the reader than a basic knowledge of sets (what is a function? what is a Cartesian product of sets?) and matrix theory (what is a linear map? what is a direct product of vector spaces?) In short, this is by far the most elementary category theory text in print. The et of core concepts of category theory are First is the ability to think with to express key concepts in terms of mappings rather than in terms of set elements. Second is the realization that collections of mathematical structures find convenient characterization in terms of arrows. Third is the use of functors as the appropriate tools with which to compare different domains of mathematical discourse.The book is divided into two parts. The first part (Chapters 1 to6) is devoted to arrows and structures, The second part (Chapters 7 to 10) is an introduction to functors.

Genres: Mathematics

185 pages, Hardcover

First published February 1, 1975

About the author

Michael A. Arbib is the Fletcher Jones Professor of Computer Science, as well as a Professor of Biological Sciences, Biomedical Engineering, Electrical Engineering, Neuroscience and Psychology at the University of Southern California.

Reviews

[Eugene · Rating 5 out of 5]

I went through a number of books and tutorials when first trying to grasp category theory, yet Chapter 1 of this book probably helped me the most. That said, the book is quite dated (that is, don't expect any references to computer science applications) and hard to find.