  We study the interaction between various analytification functors, and a
class of morphisms of rings, called homotopy epimorphisms. An analytification
functor assigns to a simplicial commutative algebra over a ring $R$, along with
a choice of Banach structure on $R$, a commutative monoid in the monoidal model
category of simplicial ind-Banach $R$-modules. We show that several
analytifications relevant to analytic geometry - such as Tate, overconvergent,
Stein analytification, and formal completion - are homotopy epimorphisms.
Another class of examples arises from Weierstrass, Laurent and rational
localisations in derived analytic geometry. As applications of this result, we
prove that Hochschild homology and the cotangent complex are computable for
analytic rings, and the computation relies only on known computations of
Hochschild homology for polynomial rings. We show that in various senses,
Hochschild homology as we define it commutes with localizations,
analytifications and completions.
