Resumen de Operadic structure on the Gerstenhaber–Schack complex for prestacks

Hoang Dinh Van, Lander Hermans, Wendy Lowen

• We introduce an operad Patch which acts on the Gerstenhaber–Schack complex of a prestack as defined by Dinh Van and Lowen, and which in particular allows us to endow this complex with an underlying L∞-structure.We make use of the operad Quilt which was used by Hawkins in order to solve the presheaf case. Due to the additional difficulty posed by the presence of twists, we have to use Quilt in a fundamentally different way (even for presheaves) in order to allow for an extension to prestacks.