  Many categories have been used to model concurrency. Using any of these, the
challenge is to reduce a given model to a smaller representation which
nevertheless preserves the relevant computer-scientific information. That is,
one wants to replace a given model with a simpler model with the same directed
homotopy-type. Unfortunately, the obvious definition of directed homotopy
equivalence is too coarse. This paper introduces the notion of context to
refine this definition.
