Theory and applications of Hopf monads

我从事霍普夫连环广告和明星自主连环广告及其应用程序的工作。首先，我理清了这两个对象之间的关系。其次，与R.Cockett一起，我们将恒星自主联合广告推广到我们所称的互补联合广告，并发展了这些理论。并应用该理论开发了一个用于并行计算的并发进程语义模型。在最后一年，但还没有结束，我一直致力于将Hopf代数的不变量推广到Hopf Monad。它们可以用来获得链和结的量子不变量。

I worked on Hopf comonads and star-autonomous comonads and their applications. First I settled the relationship between these two objects. Second, with R. Cockett, we generalized star-autonomous comonads to what we have called complementing comonads and developed the theory of these. Also, we applied this theory to develop a model of concurrent process semantics using for parallel computing. In the final year, but not yet finished, I have been working on extending invariants of Hopf algebras to Hopf monads. These can be used to obtain quantum invariants of links and knots.