The free monoidal differential modality

Richard Garner – 28 February 2024

(Joint work with JS Lemay). In this talk, I describe a result of JS and myself, which says that, for an additive symmetric monoidal category satisfying mild conditions, the forgetful functor from monoidal differential modalities to monoidal coalgebra modalities has a left adjoint. The mild conditions involve the existence of what we call "algebraically-free commutative monoids", a notion which is apparently new and interesting in its own right.