Review of Giandomenico Sica (ed.) What is Category Theory?
(DRAFT) Studia Logica 89 (2) 285-289, 2008
Giandomenico Sica’s volume is a collection of eleven papers on category theory by
philosophers, mathematicians, and mathematical physicists. In addition to papers of
direct interest to philosophers of mathematics, the volume contains some introductory
expositions of category theory along with a valuable discussion of the relationship
between category theory and physics by Bob Coecke. While there are several technically
difficult papers, the volume as a whole is reasonably accessible to those with some
familiarity with the basics of category theory. The importance of the volume lies in the
possibility that it will encourage broader interest in category theory among philosophers.
Category theory is a branch of abstract algebra devoted to investigating
transformations in a highly abstract form. In his excellent recent textbook, Steve
Awodey characterizes category theory as the “mathematical study of (abstract ) algebras
of functions. Just as group theory is the abstraction of the idea of a system of
permutations of a set of symmetries of a geometric object, category theory arises from the
idea of a system of functions among some objects.” (2006, 1) While there is obviously a
long history of reflection on the idea of transformation in geometry and algebra, the
development of abstract algebra in the 1930s permitted the study of transformations and
compositions of transformations in the most general form possible.
Giandomenico Sica’s volume is a collection of eleven papers on category theory by philosophers, mathematicians, and mathematical physicists. In addition to papers of direct interest to philosophers of mathematics, the volume contains some introductory expositions of category theory along with a valuable discussion of the relationship between category theory and physics by Bob Coecke. While there are several technically difficult papers, the volume as a whole is reasonably accessible to those with some familiarity with the basics of category theory. The importance of the volume lies in the possibility that it will encourage broader interest in category theory among philosophers.
Category theory is a branch of abstract algebra devoted to investigating transformations in a highly abstract form. In his excellent recent textbook, Steve Awodey characterizes category theory as the “mathematical study of (abstract ) algebras of functions. Just as group theory is the abstraction of the idea of a system of permutations of a set of symmetries of a geometric object, category theory arises from the idea of a system of functions among some objects.” (2006, 1) While there is obviously a long history of reflection on the idea of transformation in geometry and algebra, the development of abstract algebra in the 1930s permitted the study of transformations and compositions of transformations in the most general form possible.
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