Bridging between \"uberhomology and double homology

Abstract

We establish an isomorphism between the 0-degree \"uberhomology 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 \"uberhomology groups detect the standard simplex, and that the double homology's diagonal is related to the connected domination polynomial.