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2-CARTESIAN FIBRATIONS II: A GROTHENDIECK CONSTRUCTION FOR
$\infty $-BICATEGORIES
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- Journal:
- Journal of the Institute of Mathematics of Jussieu , First View
- Published online by Cambridge University Press:
- 02 December 2025, pp. 1-85
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- Article
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In this work, we conclude our study of fibred
$\infty $-bicategories by providing a Grothendieck construction in this setting. Given a scaled simplicial set S (which need not be fibrant) we construct a 2-categorical version of Lurie’s straightening-unstraightening adjunction, thereby furnishing an equivalence between the 
$\infty $-bicategory of 2-Cartesian fibrations over S and the 
$\infty $-bicategory of contravariant functors 
with values in the 
$\infty $-bicategory of 
$\infty $-bicategories. We provide a relative nerve construction in the case where the base is a 2-category, and use this to prove a comparison to existing bicategorical Grothendieck constructions.
with values in the 
