nLab constant sheaf

Contents

Context

$(\infty,1)$-Topos Theory

(∞,1)-topos theory

Constructions

structures in a cohesive (∞,1)-topos

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

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

from the sheaf topos to the topos Set.

Pattern

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