Dedualizing complexes of bicomodules and MGM duality over coalgebras

摘要

This paper is based on the material of Section 4 and Appendix C inarXiv:1503.05523v6, which was excluded from the subsequent versions ofarXiv:1503.05523. We present the definition of a dedualizing complex ofbicomodules over a pair of cocoherent coassociative coalgebras $\mathcal C$ and$\mathcal D$. Given such a complex $\mathcal B^\bullet$, we construct anequivalence between the (bounded or unbounded) conventional, as well asabsolute, derived categories of the abelian categories of left comodules over$\mathcal C$ and left contramodules over $\mathcal D$. Furthermore, we spellout the definition of a dedualizing complex of bisemimodules over a pair ofsemialgebras, and construct the related equivalence between the conventional orabsolute derived categories of the abelian categories of semimodules andsemicontramodules. Artinian, co-Noetherian, and cocoherent coalgebras arediscussed as a preliminary material.