Monads and distributive laws for Rota-Baxter and differential algebras

Shilong Zhang, Li Guo, William Keigher

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 we obtain monads and comonads giving the composite structures of differential and Rota-Baxter algebras. As a consequence, a mixed distributive law of the monad giving Rota-Baxter algebras over the comonad giving differential algebras is established.

Original languageEnglish (US)
Pages (from-to)139-165
Number of pages27
JournalAdvances in Applied Mathematics
StatePublished - Jan 2016

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • 12H05
  • 13Nxx
  • 16W99
  • MSC primary 18C15
  • secondary 18C20


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