Parametrized higher category theory II: Universal constructions

preprint2022arXivOpen access

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 PΣP^Σ.

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