Bridging between überhomology and double homology

We establish an isomorphism between the 0-degree überhomology and the double homology of finite simplicial complexes, using a Mayer-Vietoris spectral sequence argument. We clarify the correspondence between these theories by providing examples and some consequences; in particular, we show that überhomology groups detect the standard simplex, and that the double homology’s diagonal is related to the connected domination polynomial.