Recognizing mapping spaces

Bernard Badzioch; David Blanc; Wojciech Dorabiała

doi:10.1016/j.jpaa.2013.05.004

Recognizing mapping spaces

Bernard Badzioch, David Blanc, Wojciech Dorabiała

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

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 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 CW_AY from map_*(A, Y), inspired by Dror-Farjoun's construction of CW_A-approximations.

Original language	American English
Pages (from-to)	181-196
Number of pages	16
Journal	Journal of Pure and Applied Algebra
Volume	218
Issue number	1
DOIs	https://doi.org/10.1016/j.jpaa.2013.05.004
State	Published - Jan 2014

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jpaa.2013.05.004

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title = "Recognizing mapping spaces",

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 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.",

author = "Bernard Badzioch and David Blanc and Wojciech Dorabia{\l}a",

note = "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.",

year = "2014",

month = jan,

doi = "10.1016/j.jpaa.2013.05.004",

language = "American English",

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journal = "Journal of Pure and Applied Algebra",

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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

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VL - 218

SP - 181

EP - 196

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 1

ER -

Recognizing mapping spaces

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