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) |
|---|---|
| Pages (from-to) | 139-165 |
| Number of pages | 27 |
| Journal | Advances in Applied Mathematics |
| Volume | 72 |
| DOIs | |
| State | Published - Jan 2016 |
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All Science Journal Classification (ASJC) codes
- Applied Mathematics
Keywords
- 12H05
- 13Nxx
- 16W99
- MSC primary 18C15
- secondary 18C20
Cite this
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Monads and distributive laws for Rota-Baxter and differential algebras. / Zhang, Shilong; Guo, Li; Keigher, William.
In: Advances in Applied Mathematics, Vol. 72, 01.2016, p. 139-165.Research output: Contribution to journal › Article
TY - JOUR
T1 - Monads and distributive laws for Rota-Baxter and differential algebras
AU - Zhang, Shilong
AU - Guo, Li
AU - Keigher, William
PY - 2016/1
Y1 - 2016/1
N2 - 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.
AB - 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.
KW - 12H05
KW - 13Nxx
KW - 16W99
KW - MSC primary 18C15
KW - secondary 18C20
UR - http://www.scopus.com/inward/record.url?scp=84955140328&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84955140328&partnerID=8YFLogxK
U2 - 10.1016/j.aam.2015.09.014
DO - 10.1016/j.aam.2015.09.014
M3 - Article
AN - SCOPUS:84955140328
VL - 72
SP - 139
EP - 165
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
SN - 0196-8858
ER -