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Higher Universal Algebra in Type Theory

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If you have a question about this talk, please contact Jamie Vicary.

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 Theoretical computer science seminar series.

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