nLab
constant sheaf

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

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Definition

A constant sheaf is a sheaf (on some site C) that is isomorphic to the sheafification of a constant presheaf (a constant functor).

Together with the global section functor, the constant sheaf functor is a geometric morphism

Γ:Sh(C)Set:const \Gamma : Sh(C) \stackrel{\leftarrow}{\to} Set : const

from the sheaf topos to the topos Set.

Examples

Pattern

A locally constant sheaf / \infty-stack is also called a local system.

See also at constant presheaf.

category: sheaf theory

Revised on June 20, 2013 12:40:08 by Urs Schreiber (82.169.65.155)