We adapt the work of Power to describe general, not-necessarily composable,
not-necessarily commutative 2-categorical pasting diagrams and their composable
and commutative parts. We provide a deformation theory for pasting diagrams
valued in $k$-linear categories, paralleling that provided for diagrams of
algebras by Gerstenhaber and Schack, proving the standard results. Along the
way, the construction gives rise to a bicategorical analog of the homotopy
G-algebras of Gerstenhaber and Voronov.Comment: 31 page