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Constructive Functor

Given categories \(\mathcal{C},\mathcal{D}\), a functor \(F\colon \mathcal{C}\to\mathcal{D}\) is `conservative' if it only maps isomorphisms to isomorphisms, i.e. for \(g\) a morphism in \(\mathcal{C}\), \(F(g)\) is an isomorphism in \(\mathcal{D}\) only if \(g\) is an isomorphism in \(\mathcal{C}\).