  For a coherent site we construct a canonically associated enlarged coherent
site, such that cohomology of bounded below complexes is preserved by the
enlargement. In the topos associated to the enlarged site transfinite
compositions of epimorphisms are epimorphisms and a weak analog of the concept
of the algebraic closure exists. The construction is a variant of the work of
Bhatt and Scholze on the pro-etale topology.
