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An envelope in a category is a construction that generalizes the operations of "exterior completion", like completion of a locally convex space, or the Stone-Čech compactification of a topological space, or the universal enveloping algebra of a Lie algebra. Dually, a refinement generalizes the operations of "interior enrichment", like bornologification (or saturation) of a locally convex space, or simply connected covering of a Lie group. In this paper we define envelopes and refinements in abstract...
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