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Abstract. The class of shape equivalences for a pair (C, K) of categories is the orthogonal of K, that is Σ = K ⊥ . Then Σ is internally saturated (Σ = Σ ⊤⊥ ). On the other hand, every internally saturated class of morphisms Σ ⊂ Mor(C), is the class of shape equivalences for some pair (C, K). Moreover, every class of shape equivalences Σ enjoys a calculus of left fractions and such a fact allows one to use techniques from categories of fractions to obtain conditions for Σ ⊤ to be reflective or proreflective in C.

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