  Under mild assumptions, we construct the two Matlis additive category
equivalences for an associative ring epimorphism $u\colon R\to U$. Assuming
that the ring epimorphism is homological of flat/projective dimension $1$, we
discuss the abelian categories of $u$-comodules and $u$-contramodules and
construct the recollement of unbounded derived categories of $R$-modules,
$U$-modules, and complexes of $R$-modules with $u$-co/contramodule cohomology.
Further assumptions allow to describe the third category in the recollement as
the unbounded derived category of the abelian categories of $u$-comodules and
$u$-contramodules. For commutative rings, we also prove that any homological
epimorphism of projective dimension $1$ is flat. Injectivity of the map $u$ is
not required.
