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5 votes
1 answer
280 views

3-functoriality of the lax Gray tensor product

Alternatively, is there an obstruction to 3-functoriality or 3-naturality? … I would be interested in knowing about partial references – e.g. for the 2-functoriality of the lax Gray tensor product, and 2-naturality of the associator and unitors – if no references for the 3-functoriality
6 votes
0 answers
77 views

A distributor between categories induces a distributor between their categories of presheaves

Let $P$ be a distributor/profunctor from a small category $A$ to a small category $B$, i.e. a functor $P : B^\circ \times A \to \mathrm{Set}$. We may then define a distributor from $[A^\circ, \mathrm{ …