The category of necklaces is a test category

Arne Mertens

The category of necklaces is a test category

Category Theory 2026-07-28 v1

Authors: Arne Mertens

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.

Keywords

test category necklaces presheaves homotopy types cubical sets

Cite

@article{arxiv.2607.25399,
  title  = {The category of necklaces is a test category},
  author = {Arne Mertens},
  journal= {arXiv preprint arXiv:2607.25399},
  year   = {2026}
}

Comments

4 pages, no figures