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MARC 21

From Groups to Categorial Algebra: Introduction to Protomodular and Mal’tsev Categories
Tag	Description
020	$a9783319572192$9978-3-319-57219-2
082	$a512$223
099	$aOnline resource: Springer
100	$aBourn, Dominique.
245	$aFrom Groups to Categorial Algebra$h[EBook]$bIntroduction to Protomodular and Mal’tsev Categories /$cby Dominique Bourn.
260	$aCham :$bSpringer International Publishing :$bImprint: Birkhäuser,$c2017.
300	$aXII, 106 p.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aCompact Textbooks in Mathematics,$x2296-4568
505	$aBasic 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	$aThis 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. .
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aCompact Textbooks in Mathematics,$x2296-4568
856	$uhttp://dx.doi.org/10.1007/978-3-319-57219-2