  By endowing the \v{C}ech-de Rham complex with a Hilbert space structure, we
obtain a Hilbert complex with sufficient properties to allow for well-posed
Hodge-Laplace problems. We observe that these Hodge-Laplace equations govern a
class of coupled problems arising from physical systems including elastically
attached strings, multiple-porosity flow systems and 3D-1D coupled flow models.
