Abstract Kleisli Structures on 2-categories*

Abstract

Führmann introduced Abstract Kleisli structures to model call-by-value programming languages with side effects, and showed that they correspond to monads satisfying a certain equalising condition on the unit. We first extend this theory to non-strict morphisms of monads, and to incorporate 2-cells of monads. We then further extend this to a theory of abstract Kleisli structures on 2-categories,
characterising when the original pseudomonad can be recovered by the abstract Kleisli structure on its 2-category of free-pseudoalgebras.

Original language	English
Title of host publication	Electronic Proceedings in Theoretical Computer Science
Publication status	Accepted/In press - 6 May 2024

Embargoed Document

Adrian Miranda - Abstract Kleisli Structures on 2-categories
Accepted author manuscript, 310 KB
Licence: CC BY
Embargo ends: 14/05/25

Cite this

@inproceedings{9002d08487eb4bde99fa48e975c6645a,

title = "Abstract Kleisli Structures on 2-categories*",

abstract = "F{\"u}hrmann introduced Abstract Kleisli structures to model call-by-value programming languages with side effects, and showed that they correspond to monads satisfying a certain equalising condition on the unit. We first extend this theory to non-strict morphisms of monads, and to incorporate 2-cells of monads. We then further extend this to a theory of abstract Kleisli structures on 2-categories,characterising when the original pseudomonad can be recovered by the abstract Kleisli structure on its 2-category of free-pseudoalgebras.",

author = "Adrian Miranda",

year = "2024",

month = may,

day = "6",

language = "English",

booktitle = "Electronic Proceedings in Theoretical Computer Science",

}

TY - GEN

T1 - Abstract Kleisli Structures on 2-categories*

AU - Miranda, Adrian

PY - 2024/5/6

Y1 - 2024/5/6

N2 - Führmann introduced Abstract Kleisli structures to model call-by-value programming languages with side effects, and showed that they correspond to monads satisfying a certain equalising condition on the unit. We first extend this theory to non-strict morphisms of monads, and to incorporate 2-cells of monads. We then further extend this to a theory of abstract Kleisli structures on 2-categories,characterising when the original pseudomonad can be recovered by the abstract Kleisli structure on its 2-category of free-pseudoalgebras.

AB - Führmann introduced Abstract Kleisli structures to model call-by-value programming languages with side effects, and showed that they correspond to monads satisfying a certain equalising condition on the unit. We first extend this theory to non-strict morphisms of monads, and to incorporate 2-cells of monads. We then further extend this to a theory of abstract Kleisli structures on 2-categories,characterising when the original pseudomonad can be recovered by the abstract Kleisli structure on its 2-category of free-pseudoalgebras.

M3 - Conference contribution

BT - Electronic Proceedings in Theoretical Computer Science

ER -

Abstract

Embargoed Document

Fingerprint

Cite this