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.
Keywords: topos theory, pro-etale topology
2010 MSC: 18F10, 18F20
Theory and Applications of Categories, Vol. 31, 2016, No. 7, pp 175-200.