Involutive categories, colored $\ast$-operads and quantum field theory

Understand

Involutive category theory provides a flexible framework to describe involutive structures on algebraic objects, such as anti-linear involutions on complex vector spaces.

• Motivated by the prominent role of involutions in quantum (field) theory, we develop the involutive analogs of colored operads and their algebras, named colored $\ast$-operads and $\ast$-algebras.
• Central to the definition of colored $\ast$-operads is the involutive monoidal category of symmetric sequences, which we obtain from a general product-exponential $2$-adjunction whose right adjoint forms involutive functor categories.
• For $\ast$-algebras over $\ast$-operads we obtain involutive analogs of the usual change of color and operad adjunctions.