# Kerodon

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Notation 6.2.1.3. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between $\infty$-categories. We say that $F$ is a left adjoint, or that $F$ admits a right adjoint, if there exists a functor $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ which is right adjoint to $F$. We let $\operatorname{LFun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by those functors $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ which are left adjoints.

Let $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ be a functor between $\infty$-categories. We say that $G$ is a right adjoint, or that $G$ admits a left adjoint, if there exists a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ which is left adjoint to $G$. We let $\operatorname{RFun}( \operatorname{\mathcal{D}}, \operatorname{\mathcal{C}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{D}}, \operatorname{\mathcal{C}})$ spanned by those functors $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ which are right adjoints.