Dualizing cartesian and cocartesian fibrations

Abstract

In this technical note, we proffer a very explicit construction of the "dual cocartesian fibration" $p^{\vee }$ of a cartesian fibration $p$, and we show they are classified by the same functor to ${\mathbf{Cat}}_{\infty }$.

19 pages. Comments always welcome

References in corpus (1)

• On the Unicity of the Homotopy Theory of Higher Categories

Cited by in corpus (18)

• Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map
• Higher enveloping algebras
• On the parametrized Tate construction and two theories of real $p$-cyclotomic spectra
• Genuine equivariant factorization homology
• On quasi-categories of comodules and Landweber exactness
• Enhanced twisted arrow categories
• On rectification and enrichment of infinity properads
• A spectrum-level Hodge filtration on topological Hochschild homology
• The Beilinson regulator is a map of ring spectra
• Some Higher Coalgebra
• Infinity-operads and Day convolution in Goodwillie calculus
• Factorization homology of enriched $\infty$-categories
• Higher sheaf theory I: Correspondences
• Enhanced bivariant homology theory attached to six functor formalism
• Cartesian Factorization Systems and Grothendieck Fibrations
• The formalism of Segal sections
• On the Relation between K- and L-Theory of $C^{\ast }$-Algebras
• Recollements and stratification