basic reference for stacks

Question

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?

Answer 1

Dear professor Stasheff,

I suggest you the following papers:

1. Barbara Fantechi - Stacks for everybody, available at professor Rehmann's home page;
2. Tomás L. Gómez - Algebraic stacks, available at arxiv.org;
3. Angelo Vistoli - Notes on Grothendieck topologies, fibered categories and descent theory, available at arxiv.org.

I hope I was helpful,

best regards.

Armando