nLab
base (infinity,1)topos
Context
$(\infty,1)$Topos Theory
(∞,1)topos theory
Background
Definitions

elementary (∞,1)topos

(∞,1)site

reflective sub(∞,1)category

(∞,1)category of (∞,1)sheaves

(∞,1)topos

(n,1)topos, ntopos

(∞,1)quasitopos

(∞,2)topos

(∞,n)topos
Characterization
Morphisms
Extra stuff, structure and property

hypercomplete (∞,1)topos

over(∞,1)topos

nlocalic (∞,1)topos

locally nconnected (n,1)topos

structured (∞,1)topos

locally ∞connected (∞,1)topos, ∞connected (∞,1)topos

local (∞,1)topos

cohesive (∞,1)topos
Models
Constructions
structures in a cohesive (∞,1)topos
Contents
Idea
In ordinary topos theory it is common to “work over a fixed base topos” which may or may not be the canonical choice Set.
Similarily, in (∞,1)topos theory one may choose to work over a fixed base $(\infty,1)$topos $\mathbf{B}$ other than ∞Grpd.
Basically this amounts to working not with the (∞,1)category (∞,1)Topos, but instead in the over(∞,1)topos $(\infty,1)Topos/\mathbf{B}$.