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We observe that the category of topological space, uniform spaces, andsimplicial sets are all, in a natural way, full subcategories of the samelarger 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 thelanguage of category theory, which we hope might be of use in formalisation ofmathematics and tame topology. We formulate some arising open questions.

Topological and metric spaces are full subcategories of the category of simplicial objects of the category of filters