  In "Homotopy decomposition of classifying spaces via elementary Abelian
subgroups", Stephan Jackowski and James McClure show, for functors admitting a
Mackey complement over categories holding a direct product, a general result on
vanishing cohomology. We develop a framework leading to a general result on
trivial homotopy which partially generalizes Jackowski and McClure's result in
two different directions.
