Background
Basic concepts
equivalences in/of $(\infty,1)$-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
The generalization of the notion of accessible functor from category theory to (∞,1)-category theory.
An (∞,1)-functor $F \;\colon\; C \to D$ is accessible if $C$ is an accessible (∞,1)-category and there is a regular cardinal $\kappa$ such that $F$ preserves $\kappa$-small filtered$\,$$(\infty,1)$-colimits.
(adjoint $(\infty,1)$-functors are accessible)
If an $(\infty,1)$-functor between accessible (∞,1)-categories has a left or right adjoint (∞,1)-functor, then it is itself accessible.
Last revised on October 3, 2021 at 10:51:19. See the history of this page for a list of all contributions to it.