The grothendieck-construction tag has no wiki summary.

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### Reference request: Grothendieck construction for $\mathbb V$-distributors?

I'm currently working with an analogue of the Grothendieck construction for enriched categories:
Given a distributor a.k.a. $\mathbb V$-functor $D:X^\mathrm{op}\otimes Y\to \mathbb V$ there is a ...

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### grothendieck construction for profunctors

Given categories $X$ and $Y$ and a strong functor
$$D:X^{op}\times Y\to Cat$$
we can of course build the oplax colimit
$$\mathrm{colim}^{oplax}_{X^{op}\times Y}D$$
via the usual (covariant) ...

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### Composition of Cat-valued distributors - compatible with grothendieck construction?

Let $C$ be a category and $F\in[C^{op}, Cat]$ be a strong functor.
(1) There are functors
$$hom_C(c',c)\times F(c)\to F(c').$$
(2) The grothendieck construction gives a 2-equvalence
$$\int_C: ...

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### Strong colimits of categories.

Let $\mathcal C$ be a category and let $\mathcal F:\mathcal C\to\mathcal C\textrm{at}$ be a strong bifunctor. Given another category $\mathcal D$, let $\triangle_{\mathcal D}$ denote the constant ...

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### Reference request: 2-Grothendieck Construction

Hi Folks,
i'm looking for a reference on the 2-grothendieck construction for a functor $F:\mathcal{I}\to \mathcal{B}\mathrm{icat}$ from a bicategory $\mathcal{I}$ to the tricategory of bicategories. ...