Resumen de Recognizing mapping spaces

Bernard Badzioch, David Blanc, Wojciech Dorabiala

• Given a fixed object A in a suitable pointed simplicial model category C, we study the problem of recovering the target Y from the pointed mapping space map.(A, Y) (up to A-equivalence). We describe a recognition principle, modeled on the classical ones for loop spaces, but using the more general notion of an A-mapping algebra. It has an associated transfinite procedure for recovering CWAY from map.(A, Y), inspired by Dror-Farjoun¡¯s construction of CWA-approximations.