Orateur
Léo Hubert
Description
Grothendieck's theory of test categories allows to characterize small categories with the property that an appropriate localization of their categories of presheaves modelize the homotopy category of spaces. Any test category then allows to do homotopy theory just as well as traditional simplicial sets can.
However, simplicial sets exhibit other niceties. Among them is the Dold-Kan correspondence: simplicial abelian groups also form a model for homology types, after an appropriate localization.
In this talk, we will see how we can hunt for homotopical Dold-Kan correspondences for presheaves in abelian groups over test categories and we will give some examples, including Joyal's category Theta.
