Title: Algebraic examples of coCartesian differential monads from operads
Operads are a useful tool to classify types of algebras. To each operad is associated a monad, which in turn gives rise to a category of algebras. There is an operad for associative algebras, for commutative algebras, for Lie algebras, and the list goes on.
In this talk, we will give an introduction to operads and their algebras. We will study the notion of operadic derivation, which generalises the notion of algebraic derivation. We will define an analogue of the module of Kähler differentials for an algebra over an operad. Studying the case of free algebras over a fixed operad will allow us to build a natural derivation which equips the associated monad with the structure of a coCartesian differential monad.
This is joint work with Marcello Lanfranchi and JS Lemay.
The slides can be found at https://www.dropbox.com/s/hne867oza0fkp4v/Algebraic%20examples%20of%20coCartesian%20differential%20monads%20coming%20from%20operads.pdf?dl=0