is a generalization of a quasi-coherent sheaf on a scheme.
The most concrete description is that it is a data that consists of, for each a scheme S in the base category and
For a Deligne–Mumford stack, there is a simpler description in terms of a presentation
[1] A quasi-coherent sheaf on a Deligne–Mumford stack generalizes an orbibundle (in a sense).
Constructible sheaves (e.g., as ℓ-adic sheaves) can also be defined on an algebraic stack and they appear as coefficients of cohomology of a stack.
The following definition is (Arbarello, Cornalba & Griffiths 2011, Ch.
be a category fibered in groupoids over the category of schemes of finite type over a field with the structure functor p. Then a quasi-coherent sheaf on