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In exterior calculus on smooth manifolds, the exterior derivative and wedgeproduct are natural with respect to smooth maps between manifolds, that is,these operations commute with pullback. In discrete exterior calculus (DEC),simplicial cochains play the role of discrete forms, the coboundary operatorserves as the discrete exterior derivative, and the antisymmetrized cup productprovides a discrete wedge product. We show that these discrete operations inDEC are natural with respect to abstract simplicial maps. A second contributionis a new averaging interpretation of the discrete wedge product in DEC. We alsoshow that this wedge product is the same as Wilson's cochain product definedusing Whitney and de Rham maps.

Averaging Property of Wedge Product and Naturality in Discrete Exterior Calculus