In exterior calculus on smooth manifolds, the exterior derivative and wedge product 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 operator serves as the discrete exterior derivative, and the antisymmetrized cup product provides a discrete wedge product. We show that these discrete operations in DEC are natural with respect to abstract simplicial maps. A second contribution is a new averaging interpretation of the discrete wedge product in DEC. We also show that this wedge product is the same as Wilson's cochain product defined using Whitney and de Rham maps.

翻译：在光滑流形上的外微分中，外微分算子和楔积关于流形间的光滑映射具有自然性，即这些运算与拉回映射可交换。在离散外微分（DEC）中，单纯上链扮演离散微分形式的角色，上边界算子作为离散外微分算子，而反对称化杯积提供了离散楔积。我们证明了DEC中的这些离散运算关于抽象单纯映射具有自然性。第二个贡献是给出了DEC中离散楔积的一种新的平均诠释。同时证明了该楔积与Wilson利用Whitney映射和de Rham映射定义的上链积等价。