# Higher Universal Algebra in Type Theory

[This concludes the talk started on Tuesday 22 Jan]

I will describe recent progress on understanding higher algebraic structures in dependent type theory. In particular, I show how one can define a coherent version of polynomial monad, whose special cases include definitions of $(\infty,1)$-category and $\infty$-groupoid. I will also explain how these techniques yield a definition of simplicial type, discuss progress on formalization and formulate a number of conjectures aimed testing the definition’s suitability.

This talk is part of the Lab Lunch series.