nLab
2-pro-object

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Idea

In the context of 2-category theory, the concept of a 2-pro-object is the categorification of the concept of a pro-object. A 2-pro-object in a 2-category, 𝒞\mathcal{C}, is a 2-functor (or diagram) indexed by a 2-cofiltered 2-category. These 2-pro-objects form a 2-category, 2Pro(𝒞)2Pro(\mathcal{C}), which is closed under small 2-cofiltered pseudolimits.

Pre-composition with the inclusion c:𝒞2Pro(𝒞)c:\mathcal{C} \to 2Pro(\mathcal{C}) is an equivalence of 2-categories:

c *:Hom(2Pro(𝒞),Cat) +Hom(𝒞,Cat), c^{\ast}: Hom(2Pro(\mathcal{C}),Cat)_+ \to Hom(\mathcal{C},Cat),

where Hom(2Pro(𝒞),Cat) +Hom(2Pro(\mathcal{C}),Cat)_+ is the full subcategory whose objects are those 2-functors that preserve small 2-cofiltered pseudolimits (Descotte & Dubuc, Thrm 2.4.2).

References

Last revised on October 22, 2020 at 02:24:06. See the history of this page for a list of all contributions to it.