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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