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Pseudo-dualizing complexes of bicomodules and pairs of t-structures
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SYSNO ASEP 0554416 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Pseudo-dualizing complexes of bicomodules and pairs of t-structures Author(s) Positselski, Leonid (MU-W) SAI, ORCID, RID Source Title Applied Categorical Structures. - : Springer - ISSN 0927-2852
Roč. 30, č. 2 (2022), s. 379-416Number of pages 38 s. Language eng - English Country NL - Netherlands Keywords comodules and contramodules ; quasi-finiteness conditions ; pseudo-derived equivalences 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 000707543100001 EID SCOPUS 85117156925 DOI 10.1007/s10485-021-09660-y Annotation This paper is a coalgebra version of Positselski 'Pseudo-dualizing complexes and pseudo-derived categories' (Rendiconti Seminario Matematico Univ. Padova 143: 153–225, 2020) and a sequel to Positselski 'Dedualizing complexes of bicomodules and MGM duality over coalgebras' (Algebras and Represent Theory 21(4): 737–767, 2018). We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coassociative coalgebras C and D. For any such complex L, we construct a triangulated category endowed with a pair of (possibly degenerate) t-structures of the derived type, whose hearts are the abelian categories of left C-comodules and left D-contramodules. A weak version of pseudo-derived categories arising out of (co)resolving subcategories in abelian/exact categories with enough homotopy adjusted complexes is also considered. Quasi-finiteness conditions for coalgebras, comodules, and contramodules are discussed as a preliminary material. 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/10.1007/s10485-021-09660-y
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