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From groups to categorial algebra [electronic resource] : introduction to protomodular and Mal'tsev categories

From groups to categorial algebra [electronic resource] : introduction to protomodular and Mal'tsev categories

자료유형
E-Book(소장)
개인저자
Bourn, Dominique.
서명 / 저자사항
From groups to categorial algebra [electronic resource] : introduction to protomodular and Mal'tsev categories / Dominique Bourn.
발행사항
Cham :   Springer,   c2017.  
형태사항
1 online resource (xii, 106 p.).
총서사항
Compact Textbooks in Mathematics,2296-4568
ISBN
9783319572185 9783319572192 (e-book)
요약
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. .
일반주기
Title from e-Book title page.  
내용주기
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.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Algebra.
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URL
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020 ▼a 9783319572185
020 ▼a 9783319572192 (e-book)
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050 4 ▼a QA150-272
082 0 4 ▼a 512.2 ▼2 23
084 ▼a 512.2 ▼2 DDCK
090 ▼a 512.2
100 1 ▼a Bourn, Dominique.
245 1 0 ▼a From groups to categorial algebra ▼h [electronic resource] : ▼b introduction to protomodular and Mal'tsev categories / ▼c Dominique Bourn.
260 ▼a Cham : ▼b Springer, ▼c c2017.
300 ▼a 1 online resource (xii, 106 p.).
490 1 ▼a Compact Textbooks in Mathematics, ▼x 2296-4568
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
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. .
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Algebra.
830 0 ▼a Compact Textbooks in Mathematics.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-3-319-57219-2
945 ▼a KLPA
991 ▼a E-Book(소장)

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