nLab
(infinity,n)-sheaf

Contents

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Higher topos Theory

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Contents

Definition

For H\mathbf{H} an (∞,1)-topos and nn \in \mathbb{N}, an (,n+1)(\infty,n+1)-sheaf on (an (∞,1)-site of definition of) H\mathbf{H} is an n-fold category object in H\mathbf{H}, XnCat(H)X \in n Cat(\mathbf{H}).

See at Internal category object in an (∞,1)-category – Iterated internalization.

The collection of all (,n)(\infty,n)-sheaves is an (∞,n)-topos.

Last revised on November 27, 2012 at 13:19:25. See the history of this page for a list of all contributions to it.