Jean-Simon Pacaud Lemay - Cartesian Differential Kleisli Categories

entics:12278 - Electronic Notes in Theoretical Informatics and Computer Science, November 23, 2023, Volume 3 - Proceedings of MFPS XXXIX -
Cartesian Differential Kleisli CategoriesArticle

Authors: Jean-Simon Pacaud Lemay

    Cartesian differential categories come equipped with a differential combinator which axiomatizes the fundamental properties of the total derivative from differential calculus. The objective of this paper is to understand when the Kleisli category of a monad is a Cartesian differential category. We introduce Cartesian differential monads, which are monads whose Kleisli category is a Cartesian differential category by way of lifting the differential combinator from the base category. Examples of Cartesian differential monads include tangent bundle monads and reader monads. We give a precise characterization of Cartesian differential categories which are Kleisli categories of Cartesian differential monads using abstract Kleisli categories. We also show that the Eilenberg-Moore category of a Cartesian differential monad is a tangent category.

    Volume: Volume 3 - Proceedings of MFPS XXXIX
    Published on: November 23, 2023
    Accepted on: October 16, 2023
    Submitted on: September 15, 2023
    Keywords: Mathematics - Category Theory,Computer Science - Programming Languages,18F40, 18C20,F.3.2,F.4.1
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    • Discovery Early Career Researcher Award - Grant ID: DE230100303; Funder: Australian Research Council (ARC); Code: DE230100303
    • Funder: Natural Sciences and Engineering Research Council of Canada

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