Let $\mathcal{C}$ and $\mathcal{D}$ be categories, and write $\mathcal{C}^{\mathsf{op}}$ for the opposite category of $\mathcal{C}$ of 
.
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Given a functor
\[ F\colon \mathcal{C}\to \mathcal{D}, \]
we also write $F_{A}$ for $F\webleft (A\webright )$.
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Given a functor
\[ F\colon \mathcal{C}^{\mathsf{op}}\to \mathcal{D}, \]
we also write $F^{A}$ for $F\webleft (A\webright )$.
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Given a functor
\[ F\colon \mathcal{C}\times \mathcal{C}\to \mathcal{D}, \]
we also write $F_{A,B}$ for $F\webleft (A,B\webright )$.
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Given a functor
\[ F\colon \mathcal{C}^{\mathsf{op}}\times \mathcal{C}\to \mathcal{D}, \]
we also write $F^{A}_{B}$ for $F\webleft (A,B\webright )$.
We employ a similar notation for morphisms, writing e.g. $F_{f}$ for $F\webleft (f\webright )$ given a functor $F\colon \mathcal{C}\to \mathcal{D}$.