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:
“In my Pantheon, Pan still reigns in his pristine glory, with his ruddy face, his flowing beard, and his shaggy body, his pipe and his crook, his nymph Echo, and his chosen daughter Iambe; for the great god Pan is not dead, as was rumored. No god ever dies. Perhaps of all the gods of New England and of ancient Greece, I am most constant at his shrine.”
—Henry David Thoreau (1817–1862)