Strict stability of extension types

03/14/2022

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by   Jonathan Weinberger, et al.

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We show that the extension types occurring in Riehl–Shulman's work on synthetic (∞,1)-categories can be interpreted in the intended semantics in a way so that they are strictly stable under substitution. The splitting method used here is due to Voevodsky in 2009. It was later generalized by Lumsdaine–Warren to the method of local universes.