Monoidally graded manifolds

Shuhan Jiang

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Submission date: 07. Jun. 2022 (revised version: December 2022)
Pages: 18
Bibtex
MSC-Numbers: 58A50
Keywords and phrases: supermanifold, graded manifold, Batchelor's theorem
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Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We give a generalization of the theory of ℤ₂-graded manifolds to a theory of ℐ-graded manifolds, where ℐ is a commutative semi-ring with some additional properties. We prove Batchelor’s theorem in this generalized setting. To our knowledge, such a proof is still missing except for some special cases.