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

DOI10.1007/S10485-021-09660-YarXiv1907.03364MaRDI QIDQ6321688

Leonid Positselski

Publication date: 7 July 2019

Abstract: This paper is a coalgebra version of arXiv:1703.04266 and a sequel to arXiv:1607.03066. We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coassociative coalgebras $mathcalC$ and $mathcalD$. For any such complex $$, 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 $mathcalC$-comodules and left $mathcalD$-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.

Mathematics Subject Classification ID

Coalgebras and comodules; corings (16T15) Derived categories, triangulated categories (18G80)

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