Results 11 to 20 of about 159 (46)
Projective Covers of Flat Contramodules [PDF]
International Mathematics Research Notices, 2021 Abstract We show that a direct limit of projective contramodules (over a right linear topological ring) is projective if it has a projective cover. A similar result is obtained for $\infty $-strictly flat contramodules of projective dimension not exceeding $1$, using an argument based on the notion of the topological Jacobson radical ...
Bazzoni, S. +2 more
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General comodule-contramodule correspondence
São Paulo Journal of Mathematical Sciences, 2023 This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule categories over the original category, construct enriched functors between them and enriched adjunctions between the ...
Katerina Hristova +2 more
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Algebraic theories of power operations
Journal of Topology, Volume 16, Issue 4, Page 1543-1640, December 2023., 2023 Abstract We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well‐behaved theories of power operations for E∞$\mathbb {E}_\infty$ ring spectra.
William Balderrama
wiley +1 more source
Mixed vs Stable Anti-Yetter-Drinfeld Contramodules [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 We examine the cyclic homology of the monoidal category of modules over a finite dimensional Hopf algebra, motivated by the need to demonstrate that there is a difference between the recently introduced mixed anti-Yetter-Drinfeld contramodules and the usual stable anti-Yetter-Drinfeld contramodules. Namely, we show that Sweedler's Hopf algebra provides
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Differential graded Koszul duality: An introductory survey
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1551-1640, August 2023., 2023 Abstract This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011), no. 996, vi+133. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG‐algebras and curved DG‐coalgebras, as ...
Leonid Positselski
wiley +1 more source
Contramodules over pro-perfect topological rings [PDF]
Forum Mathematicum, 2021 Abstract For four wide classes of topological rings R \mathfrak{R} , we show that all flat left
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Matlis category equivalences for a ring epimorphism
, 2020 Under mild assumptions, we construct the two Matlis additive category equivalences for an associative ring epimorphism $u\colon R\to U$. Assuming that the ring epimorphism is homological of flat/projective dimension $1$, we discuss the abelian categories
Bazzoni, Silvana, Positselski, Leonid
core +1 more source
Contraadjusted Modules, Contramodules, and Reduced Cotorsion Modules [PDF]
Moscow Mathematical Journal, 2017 This paper is devoted to the more elementary aspects of the contramodule story, and can be viewed as an extended introduction to the more technically complicated arXiv:1503.05523. Reduced cotorsion abelian groups form an abelian category, which is in some sense covariantly dual to the category of torsion abelian groups.
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Pseudo-dualizing complexes and pseudo-derived categories
, 2020 The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by dropping the injective dimension condition, while retaining the finite generatedness and homothety isomorphism conditions.
Positselski, Leonid
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Centres, trace functors, and cyclic cohomology [PDF]
, 2020 We study the biclosedness of the monoidal categories of modules and comodules over a (left or right) Hopf algebroid, along with the bimodule category centres of the respective opposite categories and a corresponding categorical equivalence to anti Yetter-
Kowalzig, Niels
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