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Pseudo-dualizing complexes of bicomodules and pairs of t-structures

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    0554416 - MÚ 2023 RIV NL eng J - Journal Article
    Positselski, Leonid
    Pseudo-dualizing complexes of bicomodules and pairs of t-structures.
    Applied Categorical Structures. Roč. 30, č. 2 (2022), s. 379-416. ISSN 0927-2852. E-ISSN 1572-9095
    R&D Projects: GA ČR(CZ) GA20-13778S
    Institutional support: RVO:67985840
    Keywords : comodules and contramodules * quasi-finiteness conditions * pseudo-derived equivalences
    OECD category: Pure mathematics
    Impact factor: 0.713, year: 2021
    Method of publishing: Limited access

    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.
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