# Kerodon

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Notation 2.1.7.11 (The Category of Enriched Categories). Let $\operatorname{\mathcal{A}}$ be a monoidal category. We say that an $\operatorname{\mathcal{A}}$-enriched category $\operatorname{\mathcal{C}}$ is small if the collection of objects $\operatorname{Ob}(\operatorname{\mathcal{C}})$ is small. The collection of small $\operatorname{\mathcal{A}}$-enriched categories can itself be organized into a category $\operatorname{Cat}(\operatorname{\mathcal{A}})$, whose morphisms are given by $\operatorname{\mathcal{A}}$-enriched functors (in the sense of Definition 2.1.7.10).