Definition 4.34.2. Let $\mathcal{C}$ be a category.

Let $F : \mathcal{S} \to \mathcal{S}'$ be a $1$-morphism of fibred categories over $\mathcal{C}$. The

*relative inertia of $\mathcal{S}$ over $\mathcal{S}'$*is the fibred category $\mathcal{I}_{\mathcal{S}/\mathcal{S}'} \to \mathcal{C}$ of Lemma 4.34.1.By the

*inertia fibred category $\mathcal{I}_\mathcal {S}$ of $\mathcal{S}$*we mean $\mathcal{I}_\mathcal {S} = \mathcal{I}_{\mathcal{S}/\mathcal{C}}$.

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