Results 1 to 10 of about 159 (46)
Confluentes Mathematici, 2022 Contramodules are module-like algebraic structures endowed with infinite summation (or, occasionally, integration) operations satisfying natural axioms. Introduced originally by Eilenberg and Moore in 1965 in the case of coalgebras over commutative rings, contramodules experience a small renaissance now after being all but forgotten for three decades ...
Positselski, Leonid
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On the anti-Yetter–Drinfeld module-contramodule correspondence [PDF]
Journal of Noncommutative Geometry, 2019 We study a functor from anti-Yetter–Drinfeld modules to contramodules in the case of a Hopf algebra H . This functor is unpacked from the general machinery of [11]. Some byproducts of this investigation are the establishment of sufficient conditions
Brown, André EX +11 more
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Covers and direct limits: a contramodule-based approach [PDF]
Mathematische Zeitschrift, 2021 We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits, both in the categorical tilting context and beyond. In the $n$-tilting-cotilting correspondence situation, if $\mathsf A$ is a Grothendieck abelian category and the related abelian category $\mathsf B$ is equivalent to the category of ...
Silvana Bazzoni, Leonid Positselski
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Absolute algebras, contramodules, and duality squares
Journal of Pure and Applied Algebra, 2022 Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as algebras over cooperads. The goal of this article is to develop this new theory.
Lucio, Victor Roca i
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Flat comodules and contramodules as directed colimits, and cotorsion periodicity
Journal of Homotopy and Related Structures, 2023 AbstractThis paper is a follow-up to Positselski and Št’ovíček (Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity. Electronic preprint arXiv:2212.09639 [math.AG]). We consider two algebraic settings of comodules over a coring and contramodules over a topological ring with a countable base of two-sided ideals ...
Positselski, Leonid
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Categories of modules, comodules and contramodules over representations
Forum Mathematicum, 2023 Abstract We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical framework which incorporates all adjoint functors between these categories in a natural manner ...
Balodi, Mamta +2 more
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Comodules and contramodules over coalgebras associated with locally finite categories
, 2023 We explain how to attach a coalgebra $\mathcal C$ over a field $k$ to a small $k$-linear category $\mathsf E$ satisfying suitable finiteness conditions. In this context, we study full-and-faithfulness of the contramodule forgetful functor, and describe explicitly the categories of locally finite left $\mathcal C$-comodules and left $\mathcal C ...
Positselski, Leonid
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Homological full-and-faithfulness of comodule inclusion and contramodule forgetful functors
Glasgow Mathematical Journal, 2023 Abstract In this paper, we consider a conilpotent coalgebra $C$ over a field $k$ . Let $\Upsilon :\ C{{-\mathsf{Comod}}}\longrightarrow C^*{{-\mathsf{Mod}}}$ be the natural functor of inclusion of the category of $C$ -comodules into ...
Positselski, Leonid
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Contramodules for algebraic groups: the existence of mock projectives
Canadian Mathematical BulletinAbstract Let G be an affine algebraic group over an algebraically closed field of positive characteristic. Recent work of Hardesty, Nakano, and Sobaje gives necessary and sufficient conditions for the existence of so-called mock injective G-modules, that is, modules which are injective upon restriction to all Frobenius kernels of G. In this article,
Johnston, Dylan
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I denne oppgaven konstruerer vi kontramoduler, både på klassisk vis og i arbitrære lukkede symmetrisk monoidale kategorier. Vi konstruerer deretter kategoriene av komoduler og kontramoduler via kategorier av komoduler/moduler over komonader/monader.
Henrik Knudsen
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