Closed model categories for [n,m]-types

  1. Ignacio Extremiana Aldana, J. 1
  2. Hernandez Paricio, L.J. 1
  3. Rivas Rodriguez, M.T. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Theory and Applications of Categories

ISSN: 1201-561X

Año de publicación: 1997

Volumen: 3

Número: 10

Páginas: 251-266

Tipo: Artículo

SCOPUS: 2-s2.0-53249123352 GOOGLE SCHOLAR

Otras publicaciones en: Theory and Applications of Categories

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

For m >= n > 0, a map f between pointed spaces is said to be a weak [n,m]-equivalence if f induces isomorphisms of the homotopy groups \pi_k for n <= k <= m∼. Associated with this notion we give two different closed model category structures to the category of pointed spaces. Both structures have the same class of weak equivalences but different classes of fibrations and therefore of cofibrations. Using one of these structures, one obtains that the localized category is equivalent to the category of n-reduced CW-complexes with dimension less than or equal to m+1 and m-homotopy classes of cellular pointed maps. Using the other structure we see that the localized category is also equivalent to the homotopy category of (n-1)-connected (m+1)-coconnected CW-complexes.