Complexes in Cofibration Categories
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”.
KeywordsCommutative Diagram Direct Limit Full Subcategory Algebraic Topology Homotopy Category
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