%0 Journal Article %T The notion of category over an algebraic stack %A Dennis Gaitsgory %J Mathematics %D 2005 %I arXiv %X The goal of this note is to spell out the (apparently well-known and intuitively clear) notion of abelian category over an algebraic stack. In the future we will discuss the (much less evident) notion, when instead of an abelian category one considers a triangulated one. %U http://arxiv.org/abs/math/0507192v1