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Titlebook: Mal‘cev, Protomodular, Homological and Semi-Abelian Categories; Francis Borceux,Dominique Bourn Book 2004 Springer Science+Business Media

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发表于 2025-3-21 19:29:13 | 显示全部楼层 |阅读模式
书目名称Mal‘cev, Protomodular, Homological and Semi-Abelian Categories
编辑Francis Borceux,Dominique Bourn
视频video
丛书名称Mathematics and Its Applications
图书封面Titlebook: Mal‘cev, Protomodular, Homological and Semi-Abelian Categories;  Francis Borceux,Dominique Bourn Book 2004 Springer Science+Business Media
描述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.
出版日期Book 2004
关键词Abelian group; Category theory; algebra; fibrations; homology
版次1
doihttps://doi.org/10.1007/978-1-4020-1962-3
isbn_softcover978-90-481-6551-3
isbn_ebook978-1-4020-1962-3
copyrightSpringer Science+Business Media B.V. 2004
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978-90-481-6551-3Springer Science+Business Media B.V. 2004
发表于 2025-3-22 03:00:02 | 显示全部楼层
Intrinsic centrality,In this first chapter, an intrinsic notion of central morphism is introduced in the very soft algebraic context of unital categories. It reveals, inside any such category, an additive core which has a strong classification potential (see [23]).
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Homological categories,It is a classical attitude in many textbooks to prove the diagram lemmas of homo-logical algebra in the context of abelian categories. But these lemmas hold as well in, for example, the category of all groups: thus the question arises to characterize those algebraic varieties in which these lemmas are valid.
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Mathematics and Its Applicationshttp://image.papertrans.cn/m/image/622011.jpg
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Essentially affine categories,ct sense in a non pointed context. The idea has been to investigate the properties of the fibration of points which, in the pointed case, characterize the validity of the short five lemma, and to take these as a definition of protomodularity.
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