余代数上双模的去对偶复形与MGM对偶
Dedualizing complexes of bicomodules and MGM duality over coalgebras
摘要：
本文基于arXiv：1503.05523v6中第4节和附录C的材料，其被排除在arXiv：1503.05523的后续版本之外。给出了一对余凝聚余结合余代数$\mathcal C$和$\mathcal D$上双模的去对偶复形的定义.给定这样一个复$\mathcal B^\bullet$，我们构造了$\mathcal C$上的左余模和$\mathcal D$上的左逆模的阿贝尔范畴的（有界或无界）常规的以及绝对的导出范畴之间的等价。进一步，我们给出了半代数对上双半模的去对偶复形的定义，并构造了半模的阿贝尔范畴的约定或绝对导出范畴与半模的非对称范畴之间的等价关系.作为一个初步的材料，讨论了Artin，co-Noetherian，和cocoherent余代数。
英文摘要：
This paper is based on the material of Section 4 and Appendix C in arXiv:1503.05523v6, which was excluded from the subsequent versions of arXiv:1503.05523. We present the definition of a dedualizing complex of bicomodules over a pair of cocoherent coassociative coalgebras $\mathcal C$ and $\mathcal D$. Given such a complex $\mathcal B^\bullet$, we construct an equivalence between the (bounded or unbounded) conventional, as well as absolute, derived categories of the abelian categories of left comodules over $\mathcal C$ and left contramodules over $\mathcal D$. 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.
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