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arXiv · 2607.08210

Subword representations and weak hypercube dimension for acyclic categories

Isaac Carcacía-Campos
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Abstract

We introduce a categorical analogue of weak hypercube representations of finite posets by means of faithful embeddings into categories of subwords of finite words. For finite acyclic categories, we characterize those admitting such a weak subword representation: they are precisely the monic categories whose hom-sets carry a left-compatible local total order. The proof is constructive and gives an explicit word representation. We also introduce a query game for categories, generalizing a Boolean query game for posets, and show how winning sets produce explicit word representations and hence upper bounds for the weak word dimension.

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Isaac Carcacía-Campos. 2026-07-09. Subword representations and weak hypercube dimension for acyclic categories. https://arxiv.org/abs/2607.08210

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