The fibre of a pinch map in a model category
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Date
2013
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Verlag
Abstract
In the category of pointed topological spaces, let F be the homotopy fibre of the
pinching map X ∪ CA → X ∪ CA/ X from the mapping cone on a cofibration A → X
onto the suspension of A. Gray (Proc Lond Math Soc (3) 26:497–520, 1973) proved
that F is weakly homotopy equivalent to the reduced product (X, A)∞. In this paper
we prove an analogue of this phenomenon in a model category, under suitable
conditions including a cube axiom.
Description
Keywords
Model category, Reduced product, Loop object, Cube axiom
Citation
Hardie, K.A. & Witbooi, P.J. (2013). The fibre of a pinch map in a model category. Applied Categorical Structures, 21: 867 – 875.