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

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 $\mathcal{C}$ and $\mathcal{D}$. For any such complex ${\mathcal{L}}^{\bullet }$, 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.

LaTeX 2e with tikz-cd, 42 pages, 10 commutative diagrams; v.2: details and comments added in the proof of Lemma 2.6(b), two references added; v.3: references updated; v.4: the reference to arXiv:2101.10797 added; v.5: several misprints corrected; v.6: many misprints corrected, the numbering of sections shifted to agree with the journal version

References in corpus (6)

• Dedualizing complexes of bicomodules and MGM duality over coalgebras
• Contramodules over pro-perfect topological rings
• Infinity-tilting theory
• Derived, coderived, and contraderived categories of locally presentable abelian categories
• Smooth duality and co-contra correspondence
• Pseudo-dualizing complexes and pseudo-derived categories

Cited by in corpus (1)

• Homological full-and-faithfulness of comodule inclusion and contramodule forgetful functors