# Seminario: “The homotopy exact completion as an elementary quotient completion”

## Mercoledì 7 Febbraio 2018, ore 14:30 - Aula 1BC45 - Jacopo Emmenegger

ARGOMENTI: Seminari

Mercoledì 7 Febbraio 2018 alle ore 14:30 in Aula 1BC45, Jacopo Emmenegger (University of Stockholm, Sweden) terrà un seminario dal titolo “The homotopy exact completion as an elementary quotient completion”.

Abstract
Maietti and Rosolini have shown how the main exact completion constructions can be unified using the theory of doctrines, which also allows a finer description of them through more basic steps. In a recent published paper van den Berg and Moerdijk introduced a new way to construct an exact category, called the homotopy exact completion of a path category, and described three alternative ways to constructing it. This quotient completion uses homotopy theoretic concepts to provide a new categorical description of the setoid model in Martin-Loef type theory, and we will illustrate its main features using Martin-Loef type theory as an example. We will then show how this completion naturally fits into Maietti and Rosolini's framework too, and how the alternative constructions given by van den Berg and Moerdijk nicely match the basic steps isolated by Maietti and Rosolini. If time allows we will also discuss how properties of (weak) local cartesian closure behave along such steps.