Monads and distributive laws for Rota-Baxter and differential algebras

Shilong Zhang, Li Guo, William Keigher

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)139-165
Number of pages27
JournalAdvances in Applied Mathematics
Volume72
DOIs
StatePublished - Jan 2016

Fingerprint

Distributive law
Differential Algebra
Monads
Algebra
Calculus
Fundamental theorem of calculus
Differential Calculus
Composite Structures
Categorical
Multiplication
Differentiation (calculus)
Composite structures
Relationships

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Keywords

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

Cite this

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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.",
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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 journalArticle

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