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arXiv · 1303.6989

Recognizing mapping spaces

Bernard Badzioch·David Blanc·Wojciech Dorabiala
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Abstract

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 \w{\mapa(A,Y)} (up to $A$-equivalence). We describe a recognition principle, modelled on the classical ones for loop spaces, but using the more general notion of an \emph{\Ama[.]} It has an associated transfinite procedure for recovering \w{\CWA Y} from \w[,]{\mapa(A,Y)} inspired by Dror-Farjoun's construction of \ww{\CWA{}}-approximations.

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Bernard Badzioch, David Blanc, Wojciech Dorabiala. 2013-03-27. Recognizing mapping spaces. https://arxiv.org/abs/1303.6989

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