Geodesic
Closed model categories for $[n,m]$-types
Theory and applications of categories, Tome 3 (1997), pp. 251-268.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Classification : 55P15, 55U35.
Keywords: Closed model category, Homotopy category, [n, m]-types. 
@article{TAC_1997_3_a9,
     author = {J. Ignacio Extremiana Aldana and Luis J. Hernandez Paricio and Maria T. Rivas Rodriguez},
     title = {Closed model categories for $[n,m]$-types},
     journal = {Theory and applications of categories},
     pages = {251--268},
     publisher = {mathdoc},
     volume = {3},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_1997_3_a9/}
}
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J. Ignacio Extremiana Aldana; Luis J. Hernandez Paricio; Maria T. Rivas Rodriguez. Closed model categories for $[n,m]$-types. Theory and applications of categories, Tome 3 (1997), pp. 251-268. http://geodesic.mathdoc.fr/item/TAC_1997_3_a9/