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＜電子ブック＞
Mal'cev, Protomodular, Homological and Semi-Abelian Categories / by Francis Borceux, Dominique Bourn
(Mathematics and Its Applications ; 566)

版	1st ed. 2004.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2004
本文言語	英語
大きさ	XIV, 480 p : online resource
著者標目	*Borceux, Francis author Bourn, Dominique author SpringerLink (Online service)
件　名	LCSH:Algebra, Homological LCSH:Group theory LCSH:Associative rings LCSH:Associative algebras LCSH:Algebra LCSH:Topological groups LCSH:Lie groups FREE:Category Theory, Homological Algebra FREE:Group Theory and Generalizations FREE:Associative Rings and Algebras FREE:Order, Lattices, Ordered Algebraic Structures FREE:Topological Groups and Lie Groups
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4020-1962-3

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