For a ringed space (X, O), we show that the deformations of the abelian category Mod(O) of sheaves of O-modules (which can be thought of as “non-commutative spaces”) are obtained from algebroid prestacks, as introduced by Kontsevich. In case X is a quasicompact separated scheme the same is true for Qch(O), the category of quasi-coherent sheaves on X. We relate to recent work by Bressler,Gorokhovski,Nest,Tsygan.