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Pseudo-Dualizing Complexes of Bicomodules and Pairs of t-Structures

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This paper is a coalgebra version of Positselski (Rendiconti Seminario Matematico Univ. Padova 143: 153–225, 2020) and a sequel to Positselski (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 \({\mathcal {C}}\) and \({\mathcal {D}}\). For any such complex \({\mathcal {L}}^{\scriptstyle \bullet }\), 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 \({\mathcal {C}}\)-comodules and left \({\mathcal {D}}\)-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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Acknowledgements

I am grateful to Jan Št’ovíček for helpful discussions. The author’s research is supported by the GAČR project 20-13778S and research plan RVO: 67985840.

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Authors and Affiliations

  1. Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, Prague, Czech Republic

    Leonid Positselski

  2. Laboratory of Algebra and Number Theory, Institute for Information Transmission Problems, Moscow, 127051, Russia

    Leonid Positselski

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  1. Leonid Positselski
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Correspondence to Leonid Positselski.

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Communicated by Vladimir Hinich.

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Positselski, L. Pseudo-Dualizing Complexes of Bicomodules and Pairs of t-Structures. Appl Categor Struct 30, 379–416 (2022). https://doi.org/10.1007/s10485-021-09660-y

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