A multitude of metrics for learning and evaluating disentangled representations has been proposed. However, it remains unclear what these metrics truly quantify and how to compare them. To solve this problem, we introduce a systematic approach for transforming an equational definition into a quantitative metric via enriched category theory. We show how to replace (i) equality with metric, (ii) logical connectives with order operations, (iii) universal quantifier with aggregation, and (iv) existential quantifier with the best approximation. Using this approach, we can derive useful metrics for measuring the modularity and informativeness of a disentangled representation extractor.