Hardie, Keith A.Witbooi, Peter J.2018-01-102018-01-102013Hardie, K.A. & Witbooi, P.J. (2013). The fibre of a pinch map in a model category. Applied Categorical Structures, 21: 867 – 875.0927-2852http://dx.doi.org/10.1007/s10485-012-9276-5http://hdl.handle.net/10566/3371In 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.enThis is the author-version of the article published online at: http://dx.doi.org/10.1007/s10485-012-9276-5Model categoryReduced productLoop objectCube axiomArticle