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arXiv · 2404.10925

The Leibniz PROP is a crossed presimplicial algebra

Murat Can Aşkaroğulları·Atabey Kaygun
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Abstract

We prove that the Leibniz PROP is isomorphic (as $\Bbbk$-linear categories) to the symmetric crossed presimplicial algebra $\Bbbk[(\Delta^+)^{op} \mathbb{S}]$ where $\Delta^+$ is the skeletal category of finite well-ordered sets with surjections, but the distributive law between $(\Delta^+)^{op}$ and the symmetric groups $\mathbb{S} = \bigsqcup_{n\geq 1} S_n$ is not the standard one.

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Murat Can Aşkaroğulları, Atabey Kaygun. 2024-04-16. The Leibniz PROP is a crossed presimplicial algebra. https://arxiv.org/abs/2404.10925

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