∞-Dold-Kan correspondence via representation theory (Chiara Sava)Séminaire « Topologie »
Orateur : Chiara Sava
Lieu : salle des Séminaires M3
Both Happel and Ladkani proved that, for commutative rings, the quiver An is derived equivalent to the diagram generated by An where any composition of two consecutive arrows vanishes. We give a purely derivator-theoretic reformulation and proof of this result showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence provides a bridge between homotopy theory and representation theory; in fact we will see how our result is a derivator-theoretic version of the ∞-Dold-Kan correspondence for bounded cochain complexes.