# Kerodon

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Definition 8.3.3.1. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category. A $\operatorname{Hom}$-funtor for $\operatorname{\mathcal{C}}$ is a profunctor

$\mathscr {H}: \operatorname{\mathcal{C}}^{\operatorname{op}} \times \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}$

which is a covariant transport representation for twisted arrow coupling $\lambda : \operatorname{Tw}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}} \times \operatorname{\mathcal{C}}$.