Dedualizing Complexes of Bicomodules and MGM Duality Over Coalgebras

作者：Positselski Leonid^*

来源：Algebras and Representation Theory, 2018, 21(4): 737-767.

DOI：10.1007/s10468-017-9736-6

• Artinian coalgebras
• Co-Noetherian coalgebras
• Cocoherent coalgebras
• Comodules
• Contramodules
• Semialgebras
• Semimodules
• Semicontramodules
• Derived categories
• Derived comodule-contramodule correspondence
• MGM duality/equivalence
• Dedualizing complexes

We present the definition of a dedualizing complex of bicomodules over a pair of cocoherent coassociative coalgebras and . Given such a complex , we construct an equivalence between the (bounded or unbounded) conventional, as well as absolute, derived categories of the abelian categories of left comodules over and left contramodules over . Furthermore, we spell out the definition of a dedualizing complex of bisemimodules over a pair of semialgebras, and construct the related equivalence between the conventional or absolute derived categories of the abelian categories of semimodules and semicontramodules. Artinian, co-Noetherian, and cocoherent coalgebras are discussed as a preliminary material.

• 出版日期2018-8