F. William Lawvere

William F. Lawvere

Stephen Hoel Schanuel

This is an introduction to thinking about elementary mathematics from a categorial point of view. The goal is to explore the consequences of a new and fundamental insight about the nature of mathematics.

A First Introduction to Categories

Conceptual Mathematics

Stephen H. Schanuel

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics, Second Edition, introduces the concept of 'category' for the learning, development, and use of mathematics, to both beginning students and general readers, and to practicing mathematical scientists. 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.

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.

Lectures Given at a Workshop Held at SUNY, Buffalo 1982

Categories in Continuum Physics

Robert Rosebrugh

In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

F. William Lawvere

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