Results 21 to 30 of about 159 (46)
Hopf-cyclic homology with contramodule coefficients [PDF]
, 2011 A new class of coefficients for the Hopf-cyclic homology of module algebras and coalgebras is introduced. These coefficients, termed stable anti-Yetter-Drinfeld contramodules, are both modules and contramodules of a Hopf algebra that satisfy certain compatibility conditions.
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The tilting-cotilting correspondence
, 2019 To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B with a projective generator, and vice versa.
Positselski, Leonid, Stovicek, Jan
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Comodules, contramodules and Pontryagin duality
, 2018 Let $C$ be a $k$-coalgebra, where $k$ is a field. The category of pseudocompact left $C^*$-modules is dual to both the category of discrete right $C^*$-modules and to the category of left $C$-comodules. We obtain this way two sides of a square of dualities.
MacQuarrie, John, Souza, Ricardo
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Non-commutative connections of the second kind
, 2008 A connection-like objects, termed {\em hom-connections} are defined in the realm of non-commutative geometry. The definition is based on the use of homomorphisms rather than tensor products.
Connes A. +3 more
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Covering classes, strongly flat modules, and completions
, 2018 We study some closely interrelated notions of Homological Algebra: (1) We define a topology on modules over a not-necessarily commutative ring $R$ that coincides with the $R$-topology defined by Matlis when $R$ is commutative. (2) We consider the class $
Facchini, Alberto, Nazemian, Zahra
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Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence [PDF]
Memoirs of the American Mathematical Society, 2011 This paper can be thought of as an extended introduction to arXiv:0708.3398; nevertheless, most of its results are not covered by loc. cit. We consider the derived categories of DG-modules, DG-comodules, and DG-contramodules, the coderived and contraderived categories of CDG-modules, the coderived categories of CDG-comodules, and the contraderived ...
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Differential graded Koszul duality: an introductory survey
, 2022 This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir arXiv:0905.2621. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG-algebras and ...
Positselski, Leonid
core
Weakly curved A-infinity algebras over a topological local ring
, 2018 We define and study the derived categories of the first kind for curved DG and A-infinity algebras complete over a pro-Artinian local ring with the curvature elements divisible by the maximal ideal of the local ring.
Positselski, Leonid
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Journal of Algebra, 2017 We prove general results about completeness of cotorsion theories and existence of covers and envelopes in locally presentable abelian categories, extending the well-established theory for module categories and Grothendieck categories. These results are then applied to the categories of contramodules over topological rings, which provide examples and ...
Positselski, L., Rosický, J.
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, 2010 We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings).
Positselski, Leonid
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