Classification of operator extensions, monad liftings and distributive laws for differential algebras and Rota-Baxter algebras
arXiv:2002.04466 · doi:10.1142/S0219498820501728
Abstract
Generalizing the algebraic formulation of the First Fundamental Theorem of Calculus (FFTC), a class of constraints involving a pair of operators was considered in \cite{ZGK2}. For a given constraint, the existences of extensions of differential and Rota-Baxter operators, of liftings of monads and comonads, and of mixed distributive laws are shown to be equivalent. In this paper, we give a classification of the constraints satisfying these equivalent conditions.
arXiv comment25 pages. arXiv admin note: substantial text overlap with arXiv:1703.01130
References in corpus (8)
- Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
- A Unified Algebraic Approach to Classical Yang-Baxter Equation
- On Integro-Differential Algebras
- Integral Categories and Calculus Categories
- (Co)monads in Free Probability Theory
- Free integro-differential algebras and Gröbner-Shirshov bases
- Weighted Tensor Products of Joyal Species, Graphs, and Charades
- Extensions of Operators, Liftings of Monads and Distributive Laws