The category of necklaces is a test category

2026/07/28 by Arne Mertens
Mathematics · #math.CT

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Abstract

In this short note, we prove that the category of necklaces is a test category. Hence presheaves on necklaces model homotopy types. The proof is analogous to that for the category of cubes with connections.

Citations

• Nerves of enriched categories via necklaces

Related

• Presheaves of groupoids as models for homotopy types
• The category of necklaces is Reedy monoidal
• Varieties of Cubical Sets
• The homotopy category of N-complexes is a homotopy category
• Homotopical Dold-Kan Correspondences