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 *A _{X}*. 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

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**Constant Sheaf**- A Detailed Example

... The

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### Famous quotes containing the word constant:

“The thirsty earth soaks up the rain,

And drinks, and gapes for drink again.

The plants suck in the earth, and are

With *constant* drinking fresh and fair.”

—Abraham Cowley (1618–1667)