Revista de la
Unión Matemática Argentina
Functional analytic issues in $\mathbb{Z}_2^n$-geometry
Andrew James Bruce and Norbert Poncin
Volume 60, no. 2 (2019), pp. 611–636

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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.