# Central Submonads and Notions of Computation

```@article{Carette2022CentralSA,
title={Central Submonads and Notions of Computation},
author={Titouan Carette and Louis Lemonnier and Vladimir Zamdzhiev},
journal={ArXiv},
year={2022},
volume={abs/2207.09190}
}```
• Published 19 July 2022
• Mathematics
• ArXiv
The notion of "centre" has been introduced for many algebraic structures in mathematics. A notable example is the centre of a monoid which always determines a commutative submonoid. Monads in category theory are important algebraic structures that may be used to model computational eﬀects in programming languages and in this paper we show how the notion of centre may be extended to strong monads acting on symmetric monoidal categories. We show that the centre of a strong monad T , if it exists…

## References

SHOWING 1-10 OF 27 REFERENCES

### Closed categories generated by commutative monads

• A. Kock
• Mathematics
Journal of the Australian Mathematical Society
• 1971
The notion of commutative monad was defined by the author in [4]. The content of the present paper may briefly be stated: The category of algebras for a commutative monad can in a canonical way be

### Commutative Monads for Probabilistic Programming Languages

• Computer Science
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
• 2021
This paper shows how to use these monads to provide a sound and adequate denotational semantics for the Probabilistic FixPoint Calculus (PFPC) – a call-by-value simply-typed lambda calculus with mixed-variance recursive types, term recursion and probabilistic choice.

### Strong functors and monoidal monads

In [4] we proved that a commutative monad on a symmetric monoidal closed category carries the structure of a symmetric monoidal monad ([4], Theorem 3.2). We here prove the converse, so that, taken

### Categorical Monads and Computer Programming

The categorical notion of monad was first introduced into computer science as a way of structuring mathematical models of programming languages. The idea has subsequently been transferred back into

### A Categorical Approach to Probability Theory

• Computer Science, Mathematics
Stud Logica
• 2010
This work shows that the category ID of D-posets of fuzzy sets and sequentially continuous D-homomorphisms allows to characterize the passage from classical to fuzzy events as the minimal generalization having nontrivial quantum character.

### The Central Valuations Monad (Early Ideas)

• Computer Science
CALCO
• 2021
A commutative valuations monad Z is given on the category DCPO of dcpo’s and Scott-continuous functions that will be useful in giving domain-theoretic denotational semantics for statistical programming languages with continuous probabilistic choice.

### Monads on symmetric monoidal closed categories

This note is concerned with "categories with internal horn and | and we shall use the terminology from the paper [2] by EIL~.NBERG and Kv.Imy. The result proved may be stated briefly as follows : a

### Premonoidal categories and notions of computation

• Mathematics, Computer Science
Mathematical Structures in Computer Science
• 1997
The semantic definitions of Eugenio Moggi's monads are characterized as notions of computation, a representation theorem is exhibited for the premonoidal setting in terms of monads, and a fibrational setting is given for the structure.

### Universal properties of impure programming languages

• Computer Science
POPL
• 2013
It is demonstrated that type constructions for impure languages --- products, sums and functions --- can be characterized by universal properties in the setting of 'premulticategories', multicategories where the commutativity law may fail.