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.
