Parametrized higher category theory II: Universal constructions

Abstract

We develop parametrized generalizations of a number of fundamental concepts in the theory of $\infty$-categories, including factorization systems, free fibrations, exponentiable fibrations, relative colimits and relative Kan extensions, filtered and sifted diagrams, and the universal constructions Ind and $P^{\Sigma }$.

42 pages. v2: added reference to Hinich's work on promonoidal Day convolution

References in corpus (3)

• Parametrized higher category theory and higher algebra: A general introduction
• Genuine equivariant factorization homology
• Equivariant nonabelian Poincaré duality and equivariant factorization homology of Thom spectra