LEADER 04418oam 2200505 450 001 9910792054003321 005 20190911112728.0 010 $a1-299-28130-3 010 $a981-4425-92-3 035 $a(OCoLC)897557532 035 $a(MiFhGG)GVRL8QZI 035 $a(EXLCZ)992560000000099538 100 $a20130730h20132013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aHomological algebra $ein strongly non-Abelian settings /$fMarco Grandis, Universita di Genova, Italy 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2013 210 1$aNew Jersey :$cWorld Scientific,$d[2013] 210 4$d?2013 215 $a1 online resource (xi, 343 pages) $cillustrations 225 0 $aGale eBooks 300 $aDescription based upon print version of record. 311 $a981-4425-91-5 320 $aIncludes bibliographical references (p. 331-336) and index. 327 $aContents; Preface; Introduction; 0.1 Categorical settings for homological algebra; 0.2 Semiexact, homological and generalised exact categories; 0.3 Subquotients and homology; 0.4 Satellites; 0.5 Exact centres, expansions, fractions and relations; 0.6 Applications; 0.7 Homological theories and biuniversal models; 0.8 Modularity and additivity; 0.9 A list of examples; 0.10 Terminology and notation; 0.11 Acknowledgements; 1 Semiexact categories; 1.1 Some basic notions; 1.1.1 Lattices; 1.1.2 Distributive and modular lattices; 1.1.3 Galois connections; 1.1.4 Contravariant Galois connections 327 $a1.1.5 Isomorphisms, monomorphisms and epimorphisms1.1.6 Pointed categories; 1.1.7 Kernels and cokernels; 1.2 Lattices and Galois connections; 1.2.1 Definition; 1.2.2 Monos and epis; 1.2.3 Kernels and cokernels; 1.2.4 The normal factorisation; 1.2.5 Exact connections; 1.2.6 Normal monos and epis; 1.2.7 The semi-additive structure; 1.2.8 Modular connections; 1.3 The main definitions; 1.3.1 Ideals of null morphisms; 1.3.2 Closed ideals; 1.3.3 Semiexact categories; 1.3.4 Remarks; 1.3.5 Kernel duality and short exact sequences; 1.3.6 Homological and generalised exact categories; 1.3.7 Subcategories 327 $a1.4 Structural examples 1.4.1 Lattices and connections; 1.4.2 A basic homological category; 1.4.3 A p-exact category; 1.4.4 Graded objects; 1.4.5 The canonical enriched structure; 1.4.6 Proposition; 1.5 Semi-exact categories and normal subobjects; 1.5.1 Semi-exact categories and local smallness; 1.5.2 Exact sequences; 1.5.3 Lemma (Annihilation properties); 1.5.4 Theorem (Two criteria for semi-exact categories); 1.5.5 Normal factorisations and exact morphisms; 1.5.6 Direct and inverse images; 1.5.7 Lemma (Meets and detection properties); 1.5.8 Theorem and Definition (The transfer functor) 327 $a1.5.9 Remarks 1.6 Other examples of semi-exact and homological categories; 1.6.1 Groups, rings and groupoids; 1.6.2 Abelian monoids, semimodules, preordered abelian groups; 1.6.3 Topological vector spaces; 1.6.4 Pointed sets and spaces; 1.6.5 Categories of partial mappings; 1.6.6 General modules; 1.6.7 Categories of pairs; 1.6.8 Groups as pairs; 1.6.9 Two examples; 1.7 Exact functors; 1.7.0 Basic definitions; 1.7.1 Exact functors and normal subobjects; 1.7.2 Conservative exact functors; 1.7.3 Proposition and Definition (Semiexact subcategories); 1.7.4 Examples 327 $a2.2.3 Definition and Proposition (Exact ideals) 330 $aWe propose here a study of 'semiexact' and 'homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied.This is a sequel of a book on 'Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups', published by the same Editor, but can be read independently of the latter.The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell - a modera 606 $aAlgebra, Homological 606 $aHomology theory 615 0$aAlgebra, Homological. 615 0$aHomology theory. 676 $a512.64 700 $aGrandis$b Marco$0536821 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910792054003321 996 $aHomological algebra$93674833 997 $aUNINA