# Kerodon

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Construction 8.2.0.3. Let $G: \operatorname{\mathcal{C}}_{+} \rightarrow \operatorname{\mathcal{C}}_{-}$ be a functor of $\infty$-categories. Pulling back the left fibration $\operatorname{Tw}(\operatorname{\mathcal{C}}_{-} ) \rightarrow \operatorname{\mathcal{C}}_{-}^{\operatorname{op}} \times \operatorname{\mathcal{C}}_{-}$ of Proposition 8.1.1.11, we obtain a left fibration of $\infty$-categories

$\lambda _{G}: \operatorname{Tw}(\operatorname{\mathcal{C}}_{-}) \times _{ \operatorname{\mathcal{C}}_{-} } \operatorname{\mathcal{C}}_{+} \rightarrow \operatorname{\mathcal{C}}_{-}^{\operatorname{op}} \times \operatorname{\mathcal{C}}_{+},$

which we regard as a coupling of $\operatorname{\mathcal{C}}_{+}$ with $\operatorname{\mathcal{C}}_{-}$. We will refer to $\lambda _{G}$ as the coupling associated to the functor $G$.