%0 Journal Article
%T Monads and distributive laws for Rota-Baxter and differential algebras
%A Li Guo
%A William Keigher
%A Shilong Zhang
%J Mathematics
%D 2014
%I arXiv
%X In recent years, algebraic studies of the differential calculus and integral calculus in the forms of differential algebra and Rota-Baxter algebra have been merged together to reflect the close relationship between the two calculi through the First Fundamental Theorem of Calculus. In this paper we study this relationship from a categorical point of view in the context of distributive laws which can be tracked back to the distributive law of multiplication over addition. The monad giving Rota-Baxter algebras and the comonad giving differential algebras are constructed. Then a mixed distributive law of the monad over the comonad is established. As a consequence, we obtain monads and comonads giving the composite structures of differential and Rota-Baxter algebras.
%U http://arxiv.org/abs/1412.8058v2