Situation 90.29.1. Let $\Lambda$ be a Noetherian ring and let $\Lambda \to k \to l$ be a finite ring maps where $k$ and $l$ are fields. Thus $l/k$ is a finite extensions of fields. A typical object of $\mathcal{C}_{\Lambda , l}$ will be denoted $B$ and a typical object of $\mathcal{C}_{\Lambda , k}$ will be denoted $A$. We define

90.29.1.1
$$\label{formal-defos-equation-comparison} \mathcal{C}_{\Lambda , l} \longrightarrow \mathcal{C}_{\Lambda , k}, \quad B \longmapsto B \times _ l k$$

Given a category cofibred in groupoids $p : \mathcal{F} \to \mathcal{C}_{\Lambda , k}$ we obtain an associated category cofibred in groupoids

$p_{l/k} : \mathcal{F}_{l/k} \longrightarrow \mathcal{C}_{\Lambda , l}$

by setting $\mathcal{F}_{l/k}(B) = \mathcal{F}(B \times _ l k)$.

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