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From groups to categorial algebra = introduction to protomodular and Mal'tsev categories /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	From groups to categorial algebra/ by Dominique Bourn.
其他題名:	introduction to protomodular and Mal'tsev categories /
作者:	Bourn, Dominique.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xii, 106 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Group algebras. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-57219-2
ISBN:	9783319572192

From groups to categorial algebra = introduction 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

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

905294
Group algebras.

LC Class. No.: QA174.2

Dewey Class. No.: 512.2

From groups to categorial algebra = introduction to protomodular and Mal'tsev categories /
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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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