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math.CT2026
The category of necklaces is a test category
Arne Mertens
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…
math.CT2024★ 1 cited
Templicial nerve of an A-infinity category
Violeta Borges Marques, Arne Mertens
The framework of templicial vector spaces was put forth in arXiv:2302.02484v2 as a suitable generalization of simplicial sets in order to develop a theory of enriched quasi-categor…
math.CT2024
Nerves of enriched categories via necklaces
Arne Mertens
We introduce necklicial nerve functors from enriched categories to simplicial sets, which include Cordier's homotopy coherent, Lurie's differential graded and Le Grignou's cubical…