Abstract
We introduce “complexes” and “cellular objects” in cofibration categories which correspond to CW-complexes in algebraic topology. We prove a general Whitehead theorem for complexes and for cellular objects. This theorem yields as specialization most of the various Whitehead theorems proved independently in different fields of the literature. We also study the general concepts in cofibration categories which in algebraic topology correspond to the “cellular approximation theorem” and the “Blakers-Massey theorem”.
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© 1999 Springer-Verlag Berlin Heidelberg
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Baues, HJ. (1999). Complexes in Cofibration Categories. In: Combinatorial Foundation of Homology and Homotopy. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11338-7_8
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DOI: https://doi.org/10.1007/978-3-662-11338-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08447-8
Online ISBN: 978-3-662-11338-7
eBook Packages: Springer Book Archive