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July 2015 Vol. 52 No. 11

This book arose from Spivak's 2013 course at MIT, "Category Theory for Scientists," whose aim was to establish that "category theory is a powerful language for understanding and formalizing common scientific models."  Consequently, the work is less a textbook on category theory (in the spirit, say, of such old classics as those by S. Mac Lane, P. J. Freyd, B. Mitchell, B. Pareigis, or the like) than a book-length blog—or perhaps a lengthy advertorial or an extended executive overview—ruminating on how the concepts and language of category theory help researchers understand, formalize, or illustrate common scientific methods, models, and ideas across a wide range of scientific disciplines and problems.  Prospective readers expecting a textbook introduction to category theory, then, should not be shocked that the Yoneda lemma does not appear until the last 100 pages of this nearly 500-page volume, without a jot of proof. Indeed, very few theorems, properly understood, appear here at all (even fewer with proof).  But plenty of proofs are included, largely to show that the many examples provided truly represent what they were brought forth to illustrate.  There are many exercises in the book and 200 additional exercises online.  Useful reference list.

--F. E. J. Linton, emeritus, Wesleyan University

Summing Up: Recommended. Comprehensive science and mathematics collections serving upper-division undergraduates and graduate students.