Mal'cev, Protomodular, Homological and Semi-Abelian Categories

Description

The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Mal'cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint is: knowing an object, not from inside via its elements, but from outside via its relations with its environment. The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics. Front Matter ....Pages i-xiii Metatheorems (Francis Borceux, Dominique Bourn)....Pages 1-9 Intrinsic centrality (Francis Borceux, Dominique Bourn)....Pages 11-123 Mal’cev categories (Francis Borceux, Dominique Bourn)....Pages 125-228 Protomodular categories (Francis Borceux, Dominique Bourn)....Pages 229-271 Homological categories (Francis Borceux, Dominique Bourn)....Pages 273-317 Semi-abelian categories (Francis Borceux, Dominique Bourn)....Pages 319-343 Strongly protomodular categories (Francis Borceux, Dominique Bourn)....Pages 345-370 Essentially affine categories (Francis Borceux, Dominique Bourn)....Pages 371-398 Back Matter ....Pages 399-479