 PDIFF

In geometric topology, PDIFF, for "p"iecewise "diff"erentiable, is the category of piecewise-smooth manifolds and piecewise-smooth maps between them.It properly contains DIFF (the category of smooth manifolds and smooth functions between them) and PL (the category of piecewise linear manifolds and piecewise linear maps between them), and the reason it is defined is to allow one to relate these two categories.