Covers and direct limits: a contramodule-based approach
DOI10.1007/s00209-020-02654-xzbMath1492.18010arXiv1907.05537OpenAlexW3119659068WikidataQ105710847 ScholiaQ105710847MaRDI QIDQ2231124
Silvana Bazzoni, L. E. Positsel'skiĭ
Publication date: 29 September 2021
Published in: Mathematische Zeitschrift (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1907.05537
tiltingcoversprecoverspurityabelian categorycotorsion pairsdirect limitstopological modulescontramodulessmall modulescotilting\(n\)-tilting-cotilting correspondencecloseness conditionscomplete and cocomplete categoryinjective ring epimorphism
Injective modules, self-injective associative rings (16D50) Module categories in associative algebras (16D90) Torsion theories, radicals (18E40) Free, projective, and flat modules and ideals in associative algebras (16D40) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Differential graded algebras and applications (associative algebraic aspects) (16E45) Extensions of abelian groups (20K35) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Abelian categories, Grothendieck categories (18E10) Other classes of modules and ideals in associative algebras (16D80) Theories (e.g., algebraic theories), structure, and semantics (18C10) Preadditive, additive categories (18E05) Other special types of modules and ideals in commutative rings (13C13) Localization and associative Noetherian rings (16P50) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Localization of categories, calculus of fractions (18E35) Rings of fractions and localization for commutative rings (13B30) Topological categories, foundations of homotopy theory (55U40) Research exposition (monographs, survey articles) pertaining to category theory (18-02) Derived categories and commutative rings (13D09) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)
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Cites Work
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- Approximations and endomorphism algebras of modules. Volume 1: Approximations. Volume 2: Predictions.
- Tilting modules arising from ring epimorphisms.
- Covers and directed colimits.
- The countable telescope conjecture for module categories.
- Injective and flat covers, envelopes and resolvents
- Perpendicular categories with applications to representations and sheaves
- Almost perfect commutative rings
- Approximations and Mittag-Leffler conditions the tools
- Approximations and Mittag-Leffler conditions the applications
- Chain complexes and stable categories
- Flat covers of modules
- Foxby equivalence, complete modules, and torsion modules
- \(S\)-almost perfect commutative rings
- Derived decompositions of abelian categories. I
- Matlis category equivalences for a ring epimorphism
- Cotilting sheaves on Noetherian schemes
- \( \infty \)-tilting theory
- Covers, envelopes, and cotorsion theories in locally presentable abelian categories and contramodule categories
- Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves
- Intrinsic Characterizations of Some Additive Functors
- Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
- Functors on locally finitely presented additive categories
- Sheafifiable homotopy model categories
- The Tilting–Cotilting Correspondence
- FLAT RING EPIMORPHISMS OF COUNTABLE TYPE
- Modules with perfect decompositions
