Model $\infty$-categories II: Quillen adjunctions

Abstract

We prove that various structures on model $\infty$-categories descend to corresponding structures on their localizations: (i) Quillen adjunctions; (ii) two-variable Quillen adjunctions; (iii) monoidal and symmetric monoidal model structures; and (iv) enriched model structures.

References in corpus (4)

• Higher Topos Theory
• Quillen adjunctions induce adjunctions of quasicategories
• All about the Grothendieck construction
• Model $\infty$-categories I: some pleasant properties of the $\infty$-category of simplicial spaces

Cited by in corpus (3)

• Model $\infty$-categories I: some pleasant properties of the $\infty$-category of simplicial spaces
• Goerss--Hopkins obstruction theory for $\infty$-categories
• Model $\infty$-categories III: the fundamental theorem