  We observe that the category of topological space, uniform spaces, and
simplicial sets are all, in a natural way, full subcategories of the same
larger category, namely the simplicial category of filters; this is, moreover,
implicit in the definitions of a topological and uniform space.
  We use these embeddings to rewrite the notions of completeness,
precompactness, compactness, Cauchy sequence, and equicontinuity in the
language of category theory, which we hope might be of use in formalisation of
mathematics and tame topology. We formulate some arising open questions.
