2018-05-17: Thorsten Altenkirch (Nottingham)

Tue, 14 Oct 2025 16:51:42 +0000

Thorsten Altenkirch (Nottingham)

HoTT for sets

Abstract

Before getting lost in the realms of higher dimensions we should see wether we can interpret set-level HoTT. We know how to deal with functional extensionality and a static universe of propositions (see Observational Type Theory) but what about a dynamic universe of propositions, i.e. one reflecting HProps that also validates propositional extensionality. I will discuss the problems modelling this and a possible solution using globular setoids.

The dynamic prop corresponds to a subobject classifier in a topos (in particular we get unique choice) while the static universe corresponds to a quasitopos I am told.

2018-05-17 13:00:00 UTC
LT1310