Motivated by algebraic quantum field theory, I consider diagrams of algebras, i.e., functors valued in a category of associative algebras. Deformations of a diagram of algebras satisfy cubic relations and thus are not described by the quadratic Maurer-Cartan equation in a differential graded Lie algebra – suggesting the presence of an L-infinity algebra.
I describe a (differential graded) operad, Quilt, that encodes useful operations on the Hochschild bicomplex of a diagram of vector spaces. The Quilt operations generalize the brace operations for a single vector space.
Quilt extends to another operad, mQuilt, that acts on the Hochschild bicomplex of a diagram of algebras. This allows an explicit proof that the Hochschild cohomology of a diagram of algebras is a Gerstenhaber algebra.