cylinder object
Mark John Hopkins
The concept of a cylinder object in a category is an abstraction of the construction in Top which associates to any topological space the cylinder over , where is the standard topological interval. It is notably used to define the concept of left homotopy, say in a model category.
The standard topological cylinder naturally comes equipped with a continuous map
that identifies as the two ends and of the cylinder, and with a map
that collapses the cylinder back onto .
The composite of these two...