basic reference for stacks

I’d like a reference for a very basic definition of stacks
Kashiwara’s paper almost does it
except for example writing such as
for every open set U in the cover there is a cat C(U)
so U –> C(U) is a functor to the category of categories?



1 Answer


Dear professor Stasheff,

I suggest you the following paper:

Fantechi Barbara – Stacks for everybody, available at professor Rehmann’s home page;
Gأ³mez Tomأ،s L. – Algebraic stacks, available at;
Vistoli Angelo – Notes on Grothendieck topologies, fibered categories and descent theory, available at

I hope I was helpful,
best regards.