Functional analytic issues in ${\mathbb{Z}}_2^n$-Geometry

Abstract

We show that the function sheaf of a ${\mathbb{Z}}_2^n$-manifold is a nuclear Fréchet sheaf of ${\mathbb{Z}}_2^n$-graded ${\mathbb{Z}}_2^n$-commutative associative unital algebras. Further, we prove that the components of the pullback sheaf morphism of a ${\mathbb{Z}}_2^n$-morphism are all continuous. These results are essential for the existence of categorical products in the category of ${\mathbb{Z}}_2^n$-manifolds. All proofs are self-contained and explicit.

arXiv comment27 pages. Comments welcomed

Cited by in corpus (10)

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• A classification of lowest weight irreducible modules over ${\mathbb{Z}}_2^2$-graded extension of $osp(1|2)$
• Integration on minimal ${\mathbb{Z}}_2^2$-superspace and emergence of space
• Double-graded quantum superplane
• Local Forms of Morphisms of Colored Supermanifolds
• ${\mathbb{Z}}_2^2$-graded supersymmetry via superfield on minimal ${\mathbb{Z}}_2^2$-superspace
• Symplectic ${\mathbb{Z}}_2^n$-manifolds
• Principal bundles in the category of ${\mathbb{Z}}_2^n$-manifolds