nLab 2-Grothendieck construction

Idea

Generalization of the Grothendieck construction from categories to 2-categories and bicategories.

Related concepts

• $(\infty,1)$-Grothendieck construction

References

Definition of a bicategory of elements construction for pseudo-distributors/pseudo-profunctors:

• Ross Street, §1.10 of: Fibrations in bicategories, Cahiers de Topologie et Géométrie Différentielle Catégoriques, 21 2 (1980) 111-160 [numdam]

More exhaustive references:

• Igor Baković, Grothendieck construction for bicategories [pdf]

• Igor Baković, Fibrations of bicategories [pdf]

• Mitchell Buckley. Fibred 2-categories and bicategories, Journal of pure and applied algebra 218 6 (2014) 1034-1074 [doi]

With an eye towards understanding classifiers in 2-categorical logic:

• Luca Mesiti: Pointwise Kan extensions along 2-fibrations and the 2-category of elements, Theory and Applications of Categories 41 30 960–994 (2024) [arXiv:2302.04566, doi:10.70930/tac/b9u5z003]