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

## TL;DR

This paper introduces pseudo-dualizing complexes of bicomodules over coalgebras and constructs associated pairs of t-structures in derived categories, linking comodules and contramodules.

## Contribution

It defines pseudo-dualizing complexes for coalgebras and develops a framework of t-structures with hearts as categories of comodules and contramodules, extending previous algebraic concepts.

## Key findings

- Constructed triangulated categories with t-structures from pseudo-dualizing complexes.
- Established connections between comodules and contramodules via derived categories.
- Discussed conditions for quasi-finiteness in coalgebra contexts.

## 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.