Christian Sattler abstract

We try to give a categorical overview of recent work, mostly going back to Coquand and coworkers, enabling constructive homotopical interpretations of type theory in certain presheaf categories. Crucially, dependent types are interpreted as uniform fibrations, the right class in an algebraic weak factorization system. We will focus in particular on the issues of dependent products and univalent universes, giving a categorical account of the so-called glueing construction involved in the latter.

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