TY - JOUR
T1 - Recognizing mapping spaces
AU - Badzioch, Bernard
AU - Blanc, David
AU - Dorabiała, Wojciech
N1 - Funding 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.
PY - 2014/1
Y1 - 2014/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jpaa.2013.05.004
DO - 10.1016/j.jpaa.2013.05.004
M3 - Article
AN - SCOPUS:84886640808
VL - 218
SP - 181
EP - 196
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 1
ER -