Resumen de Functional analytic issues in Z ₂ⁿ-geometry

Andrew James Bruce, Norbert Poncin

• We show that the function sheaf of a Z₂ⁿ- manifold is a nuclear Fr´echet sheaf of Z₂ⁿ- graded - Z₂ⁿ commutative associative unital algebras. Further, we prove that the components of the pullback sheaf morphism of Z₂ⁿ a - morphism are all continuous. These results are essential for the existence of categorical products in the category of Z₂ⁿ -manifolds. All proofs are selfcontained and explicit.