• Prelude: Poincaré, Wittgenstein, Peirce, and the use of concepts.- Category theory in Algebraic Topology.- Category theory in Homological Algebra.- Category theory in Algebraic Geometry.- From tool to object: full-fledged category theory.- Categories as sets: problems and solutions.- Categorial foundations.- Pragmatism and category theory.

From the reviews: "Kromer provides a more complete historical study of category theory and its applications from the beginnings to about 1970. ... It caught the attention of people interested in conceptual and philosophical issues ... . I recommend Kromer's work highly to anyone who seeks to gain an understanding of category-theoretic mathematics ... . an interesting contribution to the historical philosophy of mathematical practice ... . the book is more successful as a history. It is well produced, and the English is clear enough ... ." (Jose Ferreiros, Zeitschrift fur Geschichte der Wissenschaften, Technik und Medizin, Issue 1, 2010)