nLab (2,1)-presheaf

Contents

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.

Last revised on May 4, 2021 at 15:30:04. See the history of this page for a list of all contributions to it.