LEADER 04770nam 2200637Ia 450 001 9910465423503321 005 20200520144314.0 010 $a1-299-28130-3 010 $a981-4425-92-3 035 $a(CKB)2560000000099538 035 $a(EBL)1143308 035 $a(OCoLC)830162411 035 $a(SSID)ssj0000907351 035 $a(PQKBManifestationID)11566486 035 $a(PQKBTitleCode)TC0000907351 035 $a(PQKBWorkID)10884015 035 $a(PQKB)11432131 035 $a(MiAaPQ)EBC1143308 035 $a(WSP)00002905 035 $a(PPN)189428325 035 $a(Au-PeEL)EBL1143308 035 $a(CaPaEBR)ebr10674344 035 $a(CaONFJC)MIL459380 035 $a(EXLCZ)992560000000099538 100 $a20120923d2013 uy 0 101 0 $aeng 135 $aurbuu|||uu||| 181 $ctxt 182 $cc 183 $acr 200 10$aHomological algebra$b[electronic resource] $ein strongly non-Abelian settings /$fMarco Grandis 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2013 215 $a1 online resource (356 p.) 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 608 $aElectronic books. 615 0$aAlgebra, Homological. 615 0$aHomology theory. 676 $a512.64 700 $aGrandis$b Marco$0536821 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465423503321 996 $aHomological algebra$92124128 997 $aUNINA