LEADER 04612nam 2200637 450 001 9910818938803321 005 20170918210016.0 010 $a1-4704-0645-4 035 $a(CKB)3360000000464347 035 $a(EBL)3113484 035 $a(SSID)ssj0000973903 035 $a(PQKBManifestationID)11542446 035 $a(PQKBTitleCode)TC0000973903 035 $a(PQKBWorkID)10984582 035 $a(PQKB)11479709 035 $a(MiAaPQ)EBC3113484 035 $a(RPAM)327451 035 $a(PPN)195410467 035 $a(EXLCZ)993360000000464347 100 $a20750619h19751975 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSimplicial methods and the interpretation of "triple" cohomology /$fJ. Duskin 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[1975] 210 4$dİ1975 215 $a1 online resource (145 p.) 225 1 $aMemoirs of the American Mathematical Society ;$vvolume 3, issue 2, number 163 (November 1975) 300 $aDescription based upon print version of record. 311 $a0-8218-1863-5 320 $aIncludes bibliographical references. 327 $a""TABLE OF CONTENTS""; ""ABSTRACT""; ""DEDICATION""; ""INTRODUCTION""; ""0. SIMPLICIAL OBJECTS IN CATEGORIES""; ""0.7 Verdier's Coskeleton Functor""; ""0.8 Simplicial Kernels""; ""0.11 Augmented Complexes (alternate descriptions)""; ""0.12 Contractible and Split Complexes""; ""0.13 The Augmented Coskeleton Functor""; ""0.14 Stripping or Shift Functor Dec[sup(1)]""; ""0.15 The Adjoint Pair (+,Dec[sup(1)])""; ""0.17 Nerve of a Category""; ""0.19 Homology and Cohomology""; ""1. SIMPLICIAL AND COTRIPLE COHOMOLOGY""; ""1.1 Cotriple Cohomology""; ""1.2 Non-Homogeneous Complex"" 327 $a""1.3 Triple Cohomology""""1.4 k-Boundary Systems""; ""1.5 Differential of a k-Boundary System and Cochain Reduction""; ""2. U-SPLIT AUGMENTED COMPLEXES AND THE STANDARD RESOLUTION""; ""2.6 k-Boundary System Defined by a U-Split Complex""; ""2.7 Naturality of k-Boundary Systems""; ""3. HOMOTOPY REPRESENTABILITY OF SIMPLICIAL AND COTRIPLE COHOMOLOGY -- THE EILENBERG-MAC LANE COMPLEXES K(a???, n)""; ""3.1 Definition of the Complex L(a???,n)""; ""3.2 Definition of the Complex K(a???,n)""; ""3.7 Corollary (Homotopy Representability of H[sup(n)](X.; a???) )"" 327 $a""3.8 Corollary (Homotopy Representability of H[sup(n)][sub(G)](X.a???) )""; ""3.9 Definition of the n-th cohomology groupoid H[sup(n)](X.; a???)""; ""4. K(a???,n)-T0RS0RS""; ""4.3 Morphisms of n-Torsors""; ""4.4 Change of Base""; ""4.5 Identification of K(a???,1)-torsors above X with principal a???-objects (i.e. a???-torsors) above X""; ""5. THE CHARACTERISTIC COCYCLE MAPPING Z[sup(n)][sub(G)]""; ""5.3 Functoriality of Z[sup(n)] on the Subcategory of Quasi-Coherent Morphisms""; ""6. STANDARD K(a???,n)-T0RS0R DEFINED BY AN n-COCYCLE""; ""6.1 The Standard Resolution of a a???-Algebra"" 327 $a""6.2 Cocycle Formulae""""6.3 Twisted Product Algebra Defined By a 1-Cocycle""; ""6.6.2 Alternative (Quotient) Construction of the Twisted Product Algebra Defined by a 1-cocycle""; ""6.7 Construction of the Standard K(a???,n)-Torsor Above X Defined by an n-cocycle""; ""6.8 Functor iality of S[sup(n)]( X; a???)""; ""7. THE INTERPRETATION ADJUNCTIONS""; ""7.2 The Canonical Map S[sup(n)](Z[sup(n)](X.)) a??? X.""; ""7.7 Proof That the Canonical Map f : (S[sup(n)](Z[sup(n)](X.)))[sub(n-1)] a??? (X.)[sub(n-1)] Is a Morphism of a???-Algebras""; ""8. THE INTERPRETATION BIJECTIONS (FIRST CONCLUSIONS)"" 327 $a""8.9 Theorem (Interpretation of Cotriple Cohomology)""""APPENDIX. TRIPLES, ALGEBRAS, AND TRIPLEABILITY""; ""A.2 Example: Triple Defined by a Pair of Adjoint Functors""; ""A.4 The Comparison Functor""; ""A.7 Properties""; ""A.8 Inverse Limits""; ""A.9 Tripleability Over (ENS)-Universal Algebras""; ""BIBLIOGRAPHY"" 410 0$aMemoirs of the American Mathematical Society ;$vnumber 163. 606 $aCategories (Mathematics) 606 $aTriples, Theory of 606 $aComplexes, Semisimplicial 606 $aHomology theory 615 0$aCategories (Mathematics) 615 0$aTriples, Theory of. 615 0$aComplexes, Semisimplicial. 615 0$aHomology theory. 676 $a512/.55 700 $aDuskin$b John Williford$f1937-$01640652 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910818938803321 996 $aSimplicial methods and the interpretation of "triple" cohomology$93984302 997 $aUNINA