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Applied Categorical Structures
Published in: Applied Categorical Structures 2/2022

15-10-2021

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

Author: Leonid Positselski

Published in: Applied Categorical Structures | Issue 2/2022

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Abstract

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.
previous article Split Extensions and Actions of Bialgebras and Hopf Algebras

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Metadata
Title
Pseudo-Dualizing Complexes of Bicomodules and Pairs of t-Structures
Author
Leonid Positselski
Publication date
15-10-2021
Publisher
Springer Netherlands
Published in
Applied Categorical Structures / Issue 2/2022
Print ISSN: 0927-2852
Electronic ISSN: 1572-9095
DOI
https://doi.org/10.1007/s10485-021-09660-y

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