LEADER 03345nam 22005775 450 001 9910254278803321 005 20200703083546.0 010 $a3-319-57219-9 024 7 $a10.1007/978-3-319-57219-2 035 $a(CKB)4340000000062047 035 $a(DE-He213)978-3-319-57219-2 035 $a(MiAaPQ)EBC6310835 035 $a(MiAaPQ)EBC5579286 035 $a(Au-PeEL)EBL5579286 035 $a(OCoLC)1017902785 035 $a(PPN)202992608 035 $a(EXLCZ)994340000000062047 100 $a20170613d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFrom Groups to Categorial Algebra $eIntroduction to Protomodular and Mal?tsev Categories /$fby Dominique Bourn 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (XII, 106 p.) 225 1 $aCompact Textbooks in Mathematics,$x2296-4568 311 $a3-319-57218-0 327 $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. 330 $aThis book gives a thorough and entirely self-contained, in-depth introduction to a specific approach to group theory, in a large sense of that word. The focus lie on the relationships which a group may have with other groups, via ?universal properties?, a view on that group ?from the outside?. This method of categorical algebra, is actually not limited to the study of groups alone, but applies equally well to other similar categories of algebraic objects. By introducing protomodular categories and Mal?tsev categories, which form a larger class, the structural properties of the category Gp of groups, show how they emerge from four very basic observations about the algebraic litteral calculus and how, studied for themselves at the conceptual categorical level, they lead to the main striking features of the category Gp of groups. Hardly any previous knowledge of category theory is assumed, and just a little experience with standard algebraic structures such as groups and monoids. Examples and exercises help understanding the basic definitions and results throughout the text. . 410 0$aCompact Textbooks in Mathematics,$x2296-4568 606 $aAlgebra 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 615 0$aAlgebra. 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 14$aGeneral Algebraic Systems. 615 24$aCategory Theory, Homological Algebra. 676 $a512.2 700 $aBourn$b Dominique$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767167 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254278803321 996 $aFrom Groups to Categorial Algebra$91561718 997 $aUNINA