Lawvere F.W., Schanuel S.H. Conceptual Mathematics: A First Introduction to Categories

Cambridge University Press, 1997. — 374 p. — ISBN 0-521-47249-0.The idea of a "category" - a sort of mathematical universe - has brought about a remarkable unification and simplification of mathematics. Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.