nLab
(2,1)-presheaf
Context
2-Category theory
2-category theory

Definitions
Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
$(\infty,1)$ -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 , n-topos

(∞,1)-quasitopos

(∞,2)-topos

(∞,n)-topos

Characterization
Morphisms
Extra stuff, structure and property
hypercomplete (∞,1)-topos

over-(∞,1)-topos

n-localic (∞,1)-topos

locally n-connected (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
A (2,1)-presheaf is a presheaf with values in the (2,1)-category Grpd . A 2-truncated (∞,1)-presheaf .

Sometimes this is also called a prestack . Other times a prestack is more specifically taken to be a separated (2,1)-presheaf : a $(2,1)$ -presheaf such that the functors into its descent objects are full and faithful functor s.

The ∞-stackification of a $(2,1)$ -presheaf is a certain 2-sheaf or stack .