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Closed model categories for $[n,m]$-types

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J. Ignacio Extremiana Aldana,
Luis J. Hernandez Paricio,
Maria T. Rivas Rodriguez

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.

Keywords: Closed model category, Homotopy category, [n;m]-types.

1991 MSC: 55P15, 55U35.

*Theory and Applications of Categories*, Vol. 3, 1997, No. 10, pp 251-268.

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