可邻接同调
Adjoinable Homology
摘要：
引入了两个导出函子之间的对偶性概念以及导出函子到更大范畴的扩张定理，在这些范畴中它们不需要被定义。然后应用这些思想，将余函子推广到任意余代数，并研究了余函子的性质。一个新的同调论理论，然后建立，并表现出一定的对偶关系，某些余代数的Hochschild上同调。最后，引入了一种例外类型的余代数，并利用它将这种新的同调论与这种例外代数的前有限对偶代数的连续上同调建立了明确的联系.
英文摘要：
The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext functors to an arbitrary coalgebra. A new homology theory theory is then built therefrom and is shown to exhibit certain duality relations to the Hochschild cohomology of certain coalgebras. Lastly, a certain exceptional type of coalgebra is introduced and it is used to make explicit connections between this new homology theory and the continuous cohomology of this exceptional algebra's pro-finite dual algebra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
