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Homological Algebra Notes
This note covers universal constructions, Tensor products, Injective, Projective and flat module, Homology, Resolutions, Ext and Tor, Depth, Chain maps and induced maps on Ext and tor, Ext, Tor and homological dimensions, Long exact sequences, Depth and homological dimensions, Regular local rings.
Author(s): Sean Sather Wagstaf
233 Pages 
Homological Algebra on Graded Posets
This book contains below topics, Notation and Preliminaries, A spectral sequence, Higher direct limits, Higher inverse limits, Cohomology, Application to Webbs conjecture, Application to the homotopy colimit.
Author(s): Antonio Diaz Ramos
130 Pages
Homological algebra in characteristic one
This note contains below topics, Bmodules and algebraic lattices, The category Bmod of Bmodules and the comonad, The Kleisli category Bmod2, The EilenbergMoore category Bmods of the comonad, The category Bmods and the null morphisms, Analogy with operators, Homological algebra in a homological category, The cokernel of the diagonal.
Author(s): Alain Connes, Caterina Consani
107 Pages
This note contains below topics, Preliminaries and Summary, Semialgebras and Semitensor Product, Derived Functor SemiTor, Semicontramodules and Semihomomorphisms, Derived Functor SemiExt, ComoduleContramodule Correspondence, SemimoduleSemicontramodule Correspondence, Functoriality in the Coring, Functoriality in the Semialgebra, Closed Model Category Structures, A Construction of Semialgebras, Relative Nonhomogeneous Koszul Duality, Contramodules over Coalgebras over Fields, Comparison with Arkhipov s 39 42 5 613A 45 47 2mu 6muplus1mu 603AExt 2 and Sevostyanov s 39 42 5 613A 45 47 2mu 6muplus1mu 603ATor 2, Semialgebras Associated to HarishChandra Pairs, Tate HarishChandra Pairs and Tate Lie Algebras, Groups with Open Profinite Subgroups, Algebraic Groupoids with Closed Subgroupoids.
Author(s): Leonid Positselski
310 Pages
This note covers universal constructions, Tensor products, Injective, Projective and flat module, Homology, Resolutions, Ext and Tor, Depth, Chain maps and induced maps on Ext and tor, Ext, Tor and homological dimensions, Long exact sequences, Depth and homological dimensions, Regular local rings.
Author(s): Sean Sather Wagstaf
233 Pages