**Title:** Cartesian Differential Monads

**Abstract:** Cartesian Differential Categories are defined to introduce and study the notion of differential from calculus in a category theory point of view. In a Cartesian Differential Category, morphisms between objects can be « derived », and this differentiation operation must satisfy a list of properties, including a version of the chain rule. The most predominant source of Cartesian Differential Categories is obtained by studying the free (co)algebras of a (co)monad equipped with a heavy structure – a differential storage structure – via the concept of (co)Kleisli category.

In this talk, we will introduce the notion of a Cartesian Differential (co)Monad on a Category with finite biproducts, which gives the lightest apparatus on a (co)monad which allows us to define a Cartesian Differential Category structure on its (co)Kleisli category. We will then list quantity of examples of such monads, most of which could not be given a differential storage structure, thus motivating our new construction.

This joint work with J-S Pacaud Lemay is available on the ArXiv: https://arxiv.org/abs/2108.04304

Pre-requisite: students wishing to attend the talk are welcome to do so! They should make sure they know the definition of a monad and of an algebra over a monad, a simple search on a favourite browser is probably enough.