---
title: "Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability"
authors:
  - "Tobias Fritz"
  - "Tomáš Gonda"
  - "Paolo Perrone"
  - "Eigil Fjeldgren Rischel"
year: 2023
venue: "Theoretical Computer Science"
arxiv: "2010.07416"
doi: "10.1016/j.tcs.2023.113896"
source: "https://arxiv.org/abs/2010.07416"
topics:
  - "markov-categories"
  - "categorical-probability"
  - "borel-stoch"
seed_rank: 944
seed_batch: "user-add-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 9
lineage: categorical-deep-learning
cites:
  - title: "A Survey of Graphical Languages for Monoidal Categories"
    url: "https://arxiv.org/abs/0908.3347"
    year: 2010
    arxiv: "0908.3347"
    doi: "10.1007/978-3-642-12821-9_4"
see:
  - "117-a-survey-of-graphical-languages-for-monoidal-categories"
---

# Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability

## One-sentence takeaway

Markov categories are the setting for probability; representability lets you talk about kernels to and from spaces of distributions — Weaves takes BorelStoch from here.

## Why it matters here

BorelStoch is the $B$ in Weaves' $[B;A]$. This is the probability substrate, not the array part: standard Borel spaces and measurable Markov kernels.

## Key ideas

- TCS 961:113896, 2023; arXiv:2010.07416; DOI `10.1016/j.tcs.2023.113896`.
- Recasts Blackwell–Sherman–Stein comparison of statistical experiments, plus second-order stochastic dominance, in Markov-category language.
- Representability is the extra structure that makes 'the space of distributions' an object the category can see.
- Weaves uses BorelStoch as a datatype/probability universe; it does not develop BSS.

## Caveats

## Links

- arXiv: [2010.07416](https://arxiv.org/abs/2010.07416)
- PDF: https://arxiv.org/pdf/2010.07416
- DOI: [10.1016/j.tcs.2023.113896](https://doi.org/10.1016/j.tcs.2023.113896)