Jean-Pierre Marquis has written a number of interesting and original papers on the philosophical issues related to category theory (e.g., [Marquis 1995; Marquis 1998; Landry and Marquis 2005; Marquis 2006]). His recent book incorporates a number of themes that he has previously examined, but considered from a more definite perspective: in this book his principal objective is to establish the claim that category theory is a generalization of Felix Klein’s Erlangen program. The central tenet he urges here is that category theory should be thought of in essentially geometric terms. The philosophically precise and innovative way in which he develops this thesis makes the book relevant to all those with some interest in category theory, logic, the foundations of mathematics, and more particularly the...

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