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

Samson Abramsky

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arXiv · 2206.12156

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

Samson Abramsky

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Abstract

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.

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Samson Abramsky. 2022-06-24. Notes on presheaf representations of strategies and cohomological refinements of $k$-consistency and $k$-equivalence. https://arxiv.org/abs/2206.12156

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