Cellular sheaf Laplacians on the set of simplices of symmetric simplicial set induced by hypergraph

Seongjin Choi; Junyeong Park

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arXiv · 2411.08458

Cellular sheaf Laplacians on the set of simplices of symmetric simplicial set induced by hypergraph

Seongjin Choi·Junyeong Park

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Abstract

We generalize cellular sheaf Laplacians on an ordered finite abstract simplicial complex to the set of simplices of a symmetric simplicial set. We construct a functor from the category of hypergraphs to the category of finite symmetric simplicial sets and define cellular sheaf Laplacians on the set of simplices of finite symmetric simplicial set induced by hypergraph. We provide formulas for cellular sheaf Laplacians and show that cellular sheaf Laplacian on an ordered finite abstract simplicial complex is exactly the ordered cellular sheaf Laplacian on the set of simplices induced by abstract simplicial complex.

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BibTeX RIS

Seongjin Choi, Junyeong Park. 2024-11-13. Cellular sheaf Laplacians on the set of simplices of symmetric simplicial set induced by hypergraph. https://arxiv.org/abs/2411.08458

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