In the algebraic geometry of Grothendieck, a stack refers to a sheaf of categories. In particular, a stack is a presheaf of categories in which the following descent properties (Brylinski 1993) are satisfied:

1. Given topological spaces and with a function and two sheaves and of groups on , the assignment defines a sheaf on called ;

2. Given an open subset of , a local surjective homeomorphism , and a sheaf over together with an isomorphism of sheaves over for which the left diagram above, commutes then there exists an sheaf over (unique up to isomorphism) together with an isomorphism of sheaves in such that above right diagram of sheaf isomorphisms of commutes.

Here, denotes projection onto one of the factors and denotes projection onto two of the three factors.