  We study homotopy epimorphisms and covers formulated in terms of derived
Tate's acyclicity for commutative C*-algebras and their non-Archimedean
counterparts. We prove that a homotopy epimorphism between commutative
C*-algebras precisely corresponds to a closed immersion between the compact
Hausdorff topological spaces associated to them, and a cover of a commutative
C*-algebra precisely corresponds to a topological cover of the compact
Hausdorff topological space associated to it by closed immersions admitting a
finite subcover. This permits us to prove derived and non-derived descent for
Banach modules over commutative C*-algebras.
