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arXiv · 1807.11740

Products in the category of $\mathbb{Z}_2 ^n$-manifolds

Andrew James Bruce·Norbert Poncin
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Abstract

We prove that the category of $\mathbb{Z}_2 ^n$-manifolds has all finite products. Further, we show that a $\mathbb{Z}_2 ^n$-manifold (resp., a $\mathbb{Z}_2 ^n$-morphism) can be reconstructed from its algebra of global $\mathbb{Z}_2 ^n$-functions (resp., from its algebra morphism between global $\mathbb{Z}_2 ^n$-function algebras). These results are of importance in the study of $\mathbb{Z}_2 ^n$ Lie groups. The investigation is all the more challenging, since the completed tensor product of the structure sheafs of two $\mathbb{Z}_2 ^n$-manifolds is not a sheaf. We rely on a number of results on (pre)sheaves of topological algebras, which we establish in the appendix.

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Andrew James Bruce, Norbert Poncin. 2018-07-31. Products in the category of $\mathbb{Z}_2 ^n$-manifolds. https://doi.org/10.1080/14029251.2019.1613051

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