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Derived, coderived, and contraderived categories of locally presentable abelian categories
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SYSNO ASEP 0545361 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Derived, coderived, and contraderived categories of locally presentable abelian categories Author(s) Positselski, Leonid (MU-W) SAI, ORCID, RID
Šťovíček, J. (CZ)Article number 106883 Source Title Journal of Pure and Applied Algebra. - : Elsevier - ISSN 0022-4049
Roč. 226, č. 4 (2022)Number of pages 39 s. Language eng - English Country NL - Netherlands Keywords conventional and exotic derived categories ; complete cotorsion pairs ; abelian model structures Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA20-13778S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000703984500021 EID SCOPUS 85114424531 DOI 10.1016/j.jpaa.2021.106883 Annotation For a locally presentable abelian category B with a projective generator, we construct the projective derived and contraderived model structures on the category of complexes, proving in particular the existence of enough homotopy projective complexes of projective objects. We also show that the derived category D(B) is generated, as a triangulated category with coproducts, by the projective generator of B. For a Grothendieck abelian category A, we construct the injective derived and coderived model structures on complexes. Assuming Vopěnka’s principle, we prove that the derived category D(A) is generated, as a triangulated category with products, by the injective cogenerator of A. We also define the notion of an exact category with an object size function and prove that the derived category of any such exact category with exact κ-directed colimits of chains of admissible monomorphisms has Hom sets. Hence the derived category of any locally presentable abelian category has Hom sets. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2023 Electronic address https://doi.org/10.1016/j.jpaa.2021.106883
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