# Quantifiers on languages and codensity monads

arXiv: https://arxiv.org/abs/1702.08841 · HTML: https://mlsanity.com/paper/1702.08841/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2017.

## Built on by (most cited first, 1 of 1)

- [Nominal Topology for Data Languages](https://mlsanity.com/paper/2304.13337/) (2023)

## Abstract (arXiv)

This paper contributes to the techniques of topo-algebraic recognition for languages beyond the regular setting as they relate to logic on words. In particular, we provide a general construction on recognisers corresponding to adding one layer of various kinds of quantifiers and prove a corresponding Reutenauer-type theorem. Our main tools are codensity monads and duality theory. Our construction hinges on a measure-theoretic characterisation of the profinite monad of the free S-semimodule monad for finite and commutative semirings S, which generalises our earlier insight that the Vietoris monad on Boolean spaces is the codensity monad of the finite powerset functor.