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Is the enriched bicategory of $V$-profunctors considered in the literature anywhere? Here I want $V$ to be, say, a complete, cocomplete, closed, symmetric monoidal category; and by enriched bicategory I mean $V$-enriched at the 2-cell level, or, equivalenty, $V$-cat enriched at the hom level.
At the enriched bicategory page, three of the interesting looking references are seemingly unavailable, namely Sean Carmody’s thesis, Steve Lack’s thesis and Alex Hoffnung’s notes. Does anyone know if these are online anywhere? (I realise I could email Steve or Alex, but having links from the nlab page would be even better.)
This ought to be a protoytpical example of a $V$-cat enriched bicategory, and it would be nice if someone has already proved it!
Good question, but I don’t know the answer offhand.
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