Calculating monad transformers with category theory
Category Theory
2025-03-27 v1
Authors:
Oleksandr Manzyuk
Abstract
We show that state, reader, writer, and error monad transformers are instances of one general categorical construction: translation of a monad along an adjunction.
Cite
@article{arxiv.2503.20024,
title = {Calculating monad transformers with category theory},
author = {Oleksandr Manzyuk},
journal= {arXiv preprint arXiv:2503.20024},
year = {2025}
}
Related papers
View all related →
Logic in Computer Science · Computer Science
Natural Transformations as Rewrite Rules and Monad Composition
Dexter Kozen
2023-06-22
Logic in Computer Science · Computer Science
Intersection Types for a Computational Lambda-Calculus with Global State
Ugo de'Liguoro, Riccardo Treglia
2025-09-03
Logic in Computer Science · Computer Science
A Recipe for State-and-Effect Triangles
Bart Jacobs
2023-06-22
Logic in Computer Science · Computer Science
A unified treatment of structural definitions on syntax for capture-avoiding substitution, context application, named substitution, partial differentiation, and so on
Tom Hirschowitz, Ambroise Lafont
2022-04-11
Category Theory · Mathematics
Lax monads, equipments and generalized multicategory theory
Dimitri Chikhladze
2014-12-17
Formal Languages and Automata Theory · Computer Science
Monads, Comonads, and Transducers
Rafał Stefański
2024-07-04
Logic in Computer Science · Computer Science
A Categorical Model for the Lambda Calculus with Constructors
Barbara Petit
2012-03-06
Programming Languages · Computer Science
Unifying graded and parameterised monads
Dominic Orchard, Philip Wadler, Harley Eades
2020-05-04
Logic in Computer Science · Computer Science
Extending Equational Monadic Reasoning with Monad Transformers
Reynald Affeldt, David Nowak
2021-07-20
Category Theory · Mathematics
State monads and their algebras
Francois Metayer
2007-05-23
Programming Languages · Computer Science
Implementing a Category-Theoretic Framework for Typed Abstract Syntax
Benedikt Ahrens, Ralph Matthes, Anders Mörtberg
2021-12-15
Category Theory · Mathematics
Monads, partial evaluations, and rewriting
Tobias Fritz, Paolo Perrone
2021-04-20
Logic in Computer Science · Computer Science
Monoid Structures on Indexed Containers
Michele De Pascalis, Tarmo Uustalu, Niccolò Veltrì
2025-10-01
Category Theory · Mathematics
Monads of regular theories
Stanisław Szawiel, Marek Zawadowski
2016-08-14
Machine Learning · Computer Science
Principled Understanding of Generalization for Generative Transformer Models in Arithmetic Reasoning Tasks
Xingcheng Xu, Zibo Zhao, Haipeng Zhang, Yanqing Yang
2025-08-07
Formal Languages and Automata Theory · Computer Science
On Transition Constructions for Automata -- A Categorical Perspective
Mike Cruchten
2024-06-28
Information Theory · Computer Science
A Category Theory of Communication Theory
Eric Werner
2015-05-29
Logic in Computer Science · Computer Science
Exploring the Boundaries of Monad Tensorability on Set
Nathan Bowler, Sergey Goncharov, Paul Blain Levy, Lutz Schröder
2015-07-01
Logic in Computer Science · Computer Science
Canonical Gradings of Monads
Flavien Breuvart, Dylan McDermott, Tarmo Uustalu
2023-08-01
Programming Languages · Computer Science
A Theory of Conversion Relations for Prefixed Units of Measure
Baltasar Trancón y Widemann, Markus Lepper
2025-12-31
Category Theory · Mathematics
Generalized multicategories: change-of-base, embedding, and descent
Rui Prezado, Fernando Lucatelli Nunes
2024-07-02
Programming Languages · Computer Science
Monads need not be endofunctors
Thosten Altenkirch, James Chapman, Tarmo Uustalu
2015-09-14
Programming Languages · Computer Science
From Semantics to Types: the Case of the Imperative lambda-Calculus
Ugo de'Liguoro, Riccardo Treglia
2022-02-25
Programming Languages · Computer Science
Linear usage of state
Rasmus Ejlers Møgelberg, Sam Staton
2015-07-01
Programming Languages · Computer Science
Modules over monads and operational semantics (expanded version)
André Hirschowitz, Tom Hirschowitz, Ambroise Lafont
2023-06-22