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arXiv · 2509.22968

Homotopy Theory for Ordered Simplicial Complexes

Melissa Wei
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Abstract

We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a new model for the homotopy theory of spaces.

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Melissa Wei. 2025-09-26. Homotopy Theory for Ordered Simplicial Complexes. https://arxiv.org/abs/2509.22968

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