2002/08/12 by Benoit Fresse, Benoît Fresse, Fresse, Benoit · 1 citation
Mathematics · #55P48 #55S37 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55P48 #msc:55S37
paper · pdf · doi:10.48550/arxiv.math/0208091
34 pages. I have simplified a demonstration (cf. section 5) and removed unnecessary arguments in this revised version. I have added lemma 2.4.3 which occurs in several demonstrations
openalex publication_date 2002/08/12 · arxiv created 2003/01/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The normalized cochain complex of a simplicial set N^*(Y) is endowed with the structure of an Einfinity algebra. More specifically, we prove in a previous article that N^*(Y) is an algebra over the Barratt-Eccles operad. According to M. Mandell, under reasonable completeness assumptions, this algebra structure determines the homotopy type of Y. In this article, we construct a model of the mapping space Map(X,Y). For that purpose, we extend the formalism of Lannes' T functor in the framework of Einfinity algebras. Precisely, in the category of algebras over the Barratt-Eccles operad, we have a division functor -oslash N_(X) which is left adjoint to the functor HomF(N_*(X),-). We prove that the associated left derived functor -oslashL N_*(X) is endowed with a quasi-isomorphism N^*(Y) oslashL N_*(X) --> N^* Map(X,Y).