Abstract
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 language | English (US) |
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Pages (from-to) | 139-165 |
Number of pages | 27 |
Journal | Advances in Applied Mathematics |
Volume | 72 |
DOIs | |
State | Published - Jan 2016 |
All Science Journal Classification (ASJC) codes
- Applied Mathematics
Keywords
- 12H05
- 13Nxx
- 16W99
- MSC primary 18C15
- secondary 18C20