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:
“Praise to Christ who feeds the hungry, frees the captive, finds the lost,
Heals the sick, upsets religion, fearless both of fate and cost.
Celebrate Christ’s constant presence—Friend and Stranger, Guest and Host.”
—The Iona Community (founded 1938)