Extensions of Operators, Liftings of Monads and Distributive Laws
Rings and Algebras
2020-02-12 v2 Commutative Algebra
Category Theory
Abstract
In a previous study, the algebraic formulation of the First Fundamental Theorem of Calculus (FFTC) is shown to allow extensions of differential and Rota-Baxter operators on the one hand, and to give rise to categorical explanations using the ideas of liftings of monads and comonads, and mixed distributive laws on the other. Generalizing the FFTC, we consider in this paper a class of constraints between a differential operator and a Rota-Baxter operator. For a given constraint, we show that the existences of extensions of differential and Rota-Baxter operators, of liftings of monads and comonads, and of mixed distributive laws are equivalent.
Keywords
Cite
@article{arxiv.1703.01130,
title = {Extensions of Operators, Liftings of Monads and Distributive Laws},
author = {Li Guo and William Keigher and Shilong Zhang},
journal= {arXiv preprint arXiv:1703.01130},
year = {2020}
}
Comments
18 pages. arXiv admin note: text overlap with arXiv:1412.8058