The category ${\Theta }_2$, derived modifications, and deformation theory of monoidal categories

Piergiorgio Panero, Boris Shoikhet

A complex $C^{\bullet }(C,D)(F,G)(\eta ,\theta )$, generalising the Davydov-Yetter complex of a monoidal category, is constructed. Here $C,D$ are $\mathbb{k}$-linear (dg) monoidal categories, $F,G\…