Data of enriched morphism

Remark 19.4.3. Let us spell out the data contained in an enriched morphism. The fiber of \(D^{\otimes }\) over \((\{\fa \},\{\fm \})\) is equivalent to \(C \times D\), hence we may write \(X = (A,N')\) for some \(A \in C\) and \(N' \in D\). Condition (1) says that \(\beta \) induces an isomorphism \(N' \iso N\) in \(D\). By condition (2), the morphism \(\alpha \colon X \to M\) then corresponds to a morphism \(A \otimes N \to M\) in \(D\).