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Homotopy type theory and algebraic weak factorization systems

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If you have a question about this talk, please contact Tamara von Glehn.

The theory of weak factorisation systems and Quillen model structures provides a very convenient setting to construct and analyze models of Homotopy Type Theory, most notably the simplicial model defined by Voevodsky, in which types are interpreted as Kan fibrations.

The aim of this talk is to explain how the theory of algebraic weak factorization systems provides an analogous understanding of the cubical model of Homotopy Type Theory defined by Coquand and his collaborators, in which types are interpreted as uniform Kan fibrations, i.e. fibrations equipped with a suitably coherent choice of diagonal fillers. This involves the development of a general method to construct algebraic which satisfy the so-called Frobenius property, and leads to a new proof of the right properness of the model structure for Kan complexes.

The talk is based on joint work with Christian Sattler (Leeds).

This talk is part of the Category Theory Seminar series.

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