K-theoretic obstructions to bounded t-structures
Sign Up to like & getrecommendations! Published in 2019 at "Inventiones mathematicae"
DOI: 10.1007/s00222-018-00847-0
Abstract: Schlichting conjectured that the negative K-groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree $$-1$$-1. The main results of this paper are that $$\mathrm… read more here.
Keywords: bounded structures; heart; abelian categories; theoretic obstructions ... See more keywords
Abelian Categories from Triangulated Categories via Nakaoka–Palu’s Localization
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DOI: 10.1007/s10485-021-09668-4
Abstract: The aim of this paper is to provide an expansion of Abe–Nakaoka’s heart construction to the following two different realizations of the module category over the endomorphism ring of a rigid object in a triangulated… read more here.
Keywords: categories triangulated; localization; nakaoka palu; categories via ... See more keywords
Torsion pairs in recollements of abelian categories
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DOI: 10.1007/s11464-018-0712-1
Abstract: For a recollement (A,B, C) of abelian categories, we show that torsion pairs in A and C can induce torsion pairs in B; and the converse holds true under certain conditions. read more here.
Keywords: abelian categories; recollements abelian; torsion; torsion pairs ... See more keywords
Frattini Subobjects and Extensions in Semi-Abelian Categories
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DOI: 10.1007/s41980-018-0020-2
Abstract: The purpose of this paper is to introduce Frattini theory in semi-abelian categories. We extend several basic group-theoretic results about Frattini subgroups and Frattini extensions, specifically selected from an article of Moori and Rodrigues, to… read more here.
Keywords: abelian categories; frattini subobjects; subobjects extensions; semi abelian ... See more keywords
Balance for Relative (Co)Homology in Abelian Categories
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DOI: 10.1007/s41980-019-00211-9
Abstract: Let $${\mathcal {A}}$$A be an abelian category, and $${\mathcal {X}}$$X and $${\mathcal {Y}}$$Y subcategories. We derive in this paper an additive functor $$T(-, -)$$T(-,-) using proper $${\mathcal {X}}$$X-resolutions (respectively, proper $${\mathcal {Y}}$$Y-coresolutions). Under certain conditions,… read more here.
Keywords: balance relative; relative homology; abelian categories; homology ... See more keywords
Covers, envelopes, and cotorsion theories in locally presentable abelian categories and contramodule categories
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DOI: 10.1016/j.jalgebra.2017.03.029
Abstract: 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… read more here.
Keywords: cotorsion theories; abelian categories; presentable abelian; locally presentable ... See more keywords
Compactness in abelian categories
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DOI: 10.1016/j.jalgebra.2019.05.037
Abstract: We relativize the notion of a compact object in an abelian category with respect to a fixed subclass of objects. We show that the standard closure properties persist to hold in this case. Furthermore, we… read more here.
Keywords: abelian categories; compactness abelian;
D4-objects in abelian categories: Transfer via functors
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DOI: 10.1080/00927872.2021.1964516
Abstract: Abstract We study the transfer of D4 and dually C4 objects via functors between abelian categories. We also give applications to Grothendieck categories, comodule categories, (graded) module categories. read more here.
Keywords: objects abelian; via functors; transfer via; categories transfer ... See more keywords
Auslander-Reiten duality for Grothendieck abelian categories
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DOI: 10.1090/tran/7379
Abstract: Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor Ext^1(C,-) into… read more here.
Keywords: duality; grothendieck abelian; abelian categories; auslander reiten ... See more keywords
Regular morphisms in abelian categories
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DOI: 10.1142/s0219498819501809
Abstract: We establish some properties involving regular morphisms in abelian categories. We show a decomposition theorem on the image of a regular sum of morphisms, a characterization of regular morphisms in terms of consecutive pairs of… read more here.
Keywords: regular morphisms; morphisms abelian; abelian categories; formula see ... See more keywords
Resolving resolution dimension of recollements of abelian categories
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DOI: 10.1142/s0219498821501796
Abstract: In this paper, we investigate the resolving resolution dimension with respect to the recollements of abelian categories. Let (????,ℬ,????) be a recollement of abelian categories such that ℬ and ???? have en... read more here.
Keywords: resolving resolution; abelian categories; resolution dimension; recollements abelian ... See more keywords