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grothendieck construction for profunctors

Let $f^*:= D(f, 1) $, $g_*:= D(1, g)$ then $f^* g_*= g_*f^*$, the lax.colimit is the Grothendieck construction i.e. the cofibrated category (with base $\textbf{X}^{op}\times \textbf{Y}$) associated to …
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