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A multicategory is a ... with one object?

$$ \mathcal C_0,\cdots,\mathcal C_n $$ of categories and profunctors $F_i\colon \mathcal C_{i-1}^{op}\otimes \mathcal C_i\to \mathcal V$, $G\colon \mathcal C_0^{op}\otimes \mathcal C_n \to \mathcal V$ … Of course, if $\mathcal V$ is cocomplete, then this is equivalent to the usual bicategory of $\mathcal V$-enriched profunctors. …