I will talk about joint work with Yaël Frégier about a simple construction of an L-infinity structure on the Gerstenhaber-Schack complex parametrising deformations of the diagram of algebras consisting of two algebra morphisms with the same target. Via the Maurer-Cartan formalism for L-infinity algebras, this allows one to formulate an explicit deformation?obstruction theory for deformations of the Abelian category of coherent sheaves on any smooth algebraic variety covered by two affine open sets.