Homotopy Type Theory, Higher Category Theory

我的兴趣在于范畴理论及其各种分支。我的硕士论文关注的是将范畴理论中的两个概念联系起来。其中之一是Monad，它直接适用于函数式编程。由于我一直对数学和计算的基础感兴趣，同伦型理论非常适合作为一个研究课题，所以我的目标是扩大单子和半群之间的类比，产生2-范畴的幂等完备化的概念，这将充分证明我选择研究2-范畴中的幂等元应该构成什么。此外，考察2-范畴的幂等完备性这一概念有多么相似将是很有趣的

My interests lie in category theory and its various ramifications. My master's thesis was concerned with connecting two concepts from category theory. One of these was that of a monad, which is directly applicable to functional programming. As I have always been interested in the foundations of mathematics and computation, homotopy type theory would suit me very well as a research topic so I aim to expand the analogy between monads and semigroupads, to yield a notion of idempotent completion of 2-categories, which would fully justify my choice of research on what an idempotent in a 2-category should constitute. Additionally, it would be interesting to examine how similar this notion of idempotent completeness of 2-categories