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＜E-Book＞
From Groups to Categorial Algebra : Introduction to Protomodular and Mal’tsev Categories / by Dominique Bourn
(Compact Textbooks in Mathematics. ISSN:2296455X)

Edition	1st ed. 2017.
Publisher	(Cham : Springer International Publishing : Imprint: Birkhäuser)
Year	2017
Size	XII, 106 p : online resource
Authors	*Bourn, Dominique author SpringerLink (Online service)
Subjects	LCSH:Universal algebra LCSH:Algebra, Homological FREE:General Algebraic Systems FREE:Category Theory, Homological Algebra
Notes	Basic concepts in category theory -- Internal structures -- Four basic facts in Algebra -- Unital and protomodular categories -- Regular and homological categories -- Linear and additive categories -- Mal’tsev, naturally Mal’tsev categories This book gives a thorough and entirely self-contained, in-depth introduction to a specific approach to group theory, in a large sense of that word. The focus lie on the relationships which a group may have with other groups, via “universal properties”, a view on that group “from the outside”. This method of categorical algebra, is actually not limited to the study of groups alone, but applies equally well to other similar categories of algebraic objects. By introducing protomodular categories and Mal’tsev categories, which form a larger class, the structural properties of the category Gp of groups, show how they emerge from four very basic observations about the algebraic litteral calculus and how, studied for themselves at the conceptual categorical level, they lead to the main striking features of the category Gp of groups. Hardly any previous knowledge of category theory is assumed, and just a little experience with standard algebraic structures such as groups and monoids. Examples and exercises help understanding the basic definitions and results throughout the text. HTTP:URL=https://doi.org/10.1007/978-3-319-57219-2

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