# Notes on presheaf representations of strategies and cohomological refinements of k-consistency and k-equivalence

arXiv: https://arxiv.org/abs/2206.12156 · HTML: https://mlsanity.com/paper/2206.12156/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2022.

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

- [Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework](https://mlsanity.com/paper/2505.21251/) (2025)

## Abstract (arXiv)

In this note, we show how positional strategies for k-pebble games have a natural representation as certain presheaves. These representations correspond exactly to the sheaf-theoretic models of contextuality introduced by Abramsky-Brandenburger. We study the notion of cohomological k-consistency recently introduced by Adam O' Conghaile from this perspective.