In mathematics, a constructible sheaf is a sheaf of abelian groups over some topological space X, such that X is the union of a finite number of locally closed subsets on each of which the sheaf is a locally constant sheaf. It has its origins in algebraic geometry, where in étale cohomology constructible sheaves are defined in a similar way (Artin, Grothendieck & Verdier 1972, Exposé IX § 2). For the derived category of constructible sheaves, see a section in ℓ-adic sheaf.
The finiteness theorem in étale cohomology states that the higher direct images of a constructible sheaf are constructible.