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

2004. Auflage 2004
ISBN: 978-1-4020-1961-6
Verlag: Springer

Buch, Englisch, 480 Seiten, Format (B × H): 161 mm x 241 mm, Gewicht: 1920 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Borceux, Francis

Bourn, Dominique

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

From the contents:

Preface. Metatheorems.- 1 Intrinsic centrality.- 2 Mal’cev categories.- 3 Protomodular categories.- 4 Homological categories.- 5 Semi-abelian categories.- 6 Strongly protomodular categories.- 7 Essentially affine categories.- Appendix.-Classification table of the fibration of points. Bibliography. Index of symbols. Index of definitions.