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.
Bibliographical noteFunding Information:
The authors wish to thank Boris Chorny for useful comments on this paper, and the referee for many detailed and pertinent remarks. The second author was partially supported by Israel Science Foundation grant 74/11.
ASJC Scopus subject areas
- Algebra and Number Theory