nLab
hypercompletion

Context

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

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Contents

Idea

The hypercompletion (Lurie) or tt-completion (Rezk, ToënVezzosi) of an (∞,1)-topos of (∞,1)-sheaves is a further localization/(∞,1)-sheafification which corresponds to retaining only those (∞,1)-sheaves which satisfy descent with respect to all hypercovers.

Definition

Definition

An (∞,1)-topos of (∞,1)-sheaves is a hypercomplete (∞,1)-topos if every \infty-connective morphism is an equivalence.

Remark

This may be read as saying that the Whitehead theorem is valid in the (∞,1)-topos.

Examples

References

Section 10 of

Section 6.5 of

Revised on September 25, 2013 10:05:17 by Tim Porter (95.147.236.8)