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

Abstract

This paper is a coalgebra version of [23] and a sequel to [21]. We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coassociative coalgebras C and D. For any such complex L • , 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 C-comodules and left 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. Contents 27 5. Minimal Corresponding Classes 29 6. Dualizing Complexes 31 7. Dedualizing Complexes 37 8. Main Diagram 38 References 40