In mathematics, the constant sheaf on a topological space X associated to a set A is a sheaf of sets on X whose stalks are all equal to A. It is denoted by A or AX. The constant presheaf with value A is the presheaf that assigns to each open subset of X the value A, and all of whose restriction maps are the identity map A → A. The constant sheaf associated to A is the sheafification of the constant presheaf associated to A.
In certain cases, the set A may be replaced with an object A in some category C (e.g. when C is the category of abelian groups, or commutative rings).
Constant sheaves of abelian groups appear in particular as coefficients in sheaf cohomology.
Read more about Constant Sheaf: Basics, A Detailed Example
Famous quotes containing the word constant:
“For centuries the death penalty, often accompanied by barbarous refinements, has been trying to hold crime in check; yet crime persists. Why? Because the instincts that are warring in man are not, as the law claims, constant forces in a state of equilibrium.”
—Albert Camus (1913–1960)