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arXiv · 1801.07235

The cylinder of a relation and generalized versions of the Nerve Theorem

Ximena Fernández·Elias Gabriel Minian
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Abstract

We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen's Theorem A for order preserving maps, and derive novel formulations of the classical Nerve Theorem for posets and simplicial complexes, suitable for covers with not necessarily contractible intersections.

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Ximena Fernández, Elias Gabriel Minian. 2018-01-22. The cylinder of a relation and generalized versions of the Nerve Theorem. https://arxiv.org/abs/1801.07235

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