# nLab (2,1)-presheaf

### Context

#### 2-Category theory

2-category theory

## Structures on 2-categories

#### $(\infty,1)$-Topos Theory

(∞,1)-topos theory

## 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 functors.

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

Revised on November 18, 2012 02:21:18 by Noam Zeilberger (192.16.204.218)