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Constructive Homological Algebra and Applications
This note contains below topics, Standard Homological Algebra, Spectral sequences, Effective homology, Constructive Homology and Commutative Algebra, Effective homology of Koszul complexes, Simplicial sets, Serre spectral sequence, The EilenbergMoore spectral sequence, The claimed Postnikov invariants This section is a rough copy of the paper RBSR8 which explains some redundancies and also some gaps with respect to the previous sections in spite of these defects we think a reader having reached this point of the text could be interested by this section making obvious a surrealist error in the standard terminology of Algebraic Topology.
Author(s): Julio Rubio, Francis Sergeraert
154 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