Cover image for Conceptual mathematics : a first introduction to categories
Conceptual mathematics : a first introduction to categories
Lawvere, F. W.
Personal Author:
Publication Information:
Cambridge ; New York, NY, USA : Cambridge University Press, [1997]

Physical Description:
xii, 358 pages : illustrations ; 26 cm
General Note:
Includes index.

Format :


Call Number
Material Type
Home Location
Item Holds
QA169 .L355 1997 Adult Non-Fiction Non-Fiction Area

On Order



In the last fifty years, the use of the notion of 'category' has led to a remarkable unification and simplification of mathematics. Written by two of the best known participants in this development, Conceptual Mathematics is the first book to serve 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. While the ideas and techniques of basic category theory are useful throughout modern mathematics, this book does not presuppose knowledge of specific fields but rather develops elementary categories such as directed graphs and discrete dynamical systems from the beginning. The fundamental ideas are then illuminated in an engaging way by examples in these categories.

Reviews 1

Choice Review

The foundational force of category theory has reshaped nearly every branch of mathematics during the 20th century but has as yet hardly touched the undergraduate curriculum. Paradoxically, this mathematical theory of "natural" constructions still seems unnatural and exotic to many research mathematicians who, specializing in other areas, habitually think in set-theoretic terms and only learn category theory as a "second language." Lawvere and Schanuel, two major category theory pioneers, believe in learning this new way of thinking right from the start and have addressed this book not merely to undergraduate mathematics majors, but even to the general reader! Perforce, they cannot assume prior familiarity with the broad range of mathematical structures that comprise the categories that form the examples and provide the motivation for the standard expositions of this subject, but they go very far with examples that they can build from first principles (involving ideas like sets, graphs, and dynamical systems), and they even get as far as toposes! One hopes that, among others, this book will come to the attention of those involved with teacher education! For all libraries. D. V. Feldman; University of New Hampshire

Table of Contents

Please read this
Note to the reader
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