2-范畴与循环同调
2-categories and cyclic homology
摘要：
本论文的题目是余单分布律在循环同调理论中的应用。解释，我们的主要目的是：1）研究如何循环同调的结合代数和霍普夫代数在原来的意义上的Connes和Moscovici产生的分配律，并澄清的作用，不同的概念bimonad在这一推广。2)将有单位的结合代数的循环同调的扭曲过程推广到由分配律定义的任何对偶对象。3)研究玻姆和斯特凡的方法来构建duplicial对象的普遍性，我们这样做的一个2-范畴推广的Hochschild（上）同调。4)去研究那些神经具有双重结构的范畴。
英文摘要：
The topic of this thesis is the application of distributive laws between comonads to the theory of cyclic homology. Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the original sense of Connes and Moscovici arises from a distributive law, and to clarify the role of different notions of bimonad in this generalisation. 2) To extend the procedure of twisting the cyclic homology of a unital associative algebra to any duplicial object defined by a distributive law. 3) To study the universality of Bohm and Stefan's approach to constructing duplicial objects, which we do in terms of a 2-categorical generalisation of Hochschild (co)homology. 4) To characterise those categories whose nerve admits a duplicial structure.
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。
