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From groups to categorial algebraint...

Bourn, Dominique.

From groups to categorial algebraintroduction to protomodular and Mal'tsev categories /

Record Type:	Electronic resources : Monograph/item
Title/Author:	From groups to categorial algebraby Dominique Bourn.
Reminder of title:	introduction to protomodular and Mal'tsev categories /
Author:	Bourn, Dominique.
Published:	Cham :Springer International Publishing :2017.
Description:	xii, 106 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Group algebras.
Online resource:	http://dx.doi.org/10.1007/978-3-319-57219-2
ISBN:	9783319572192$q(electronic bk.)

From groups to categorial algebraintroduction to protomodular and Mal'tsev categories /
Bourn, Dominique.

From groups to categorial algebraintroduction to protomodular and Mal'tsev categories /[electronic resource] :by Dominique Bourn. - Cham :Springer International Publishing :2017. - xii, 106 p. :ill., digital ;24 cm. - Compact textbooks in mathematics,2296-4568. - Compact textbooks in mathematics..

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.

ISBN: 9783319572192$q(electronic bk.)

Standard No.: 10.1007/978-3-319-57219-2doiSubjects--Topical Terms:

663639
Group algebras.

LC Class. No.: QA174.2

Dewey Class. No.: 512.2

From groups to categorial algebraintroduction to protomodular and Mal'tsev categories /
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490 1 $a Compact textbooks in mathematics, $x 2296-4568
505 0 $a 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.
520 $a 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.
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