Linear ℤⁿ₂ -Manifolds and Linear Actions

Abstract

We establish the representability of the general linear ℤⁿ₂-group and use the restricted functor of points – whose test category is the category of ℤⁿ₂-manifolds over a single topological point – to define its smooth linear actions on ℤⁿ₂-graded vector spaces and linear ℤⁿ₂-manifolds. Throughout the paper, particular emphasis is placed on the full faithfulness and target category of the restricted functor of points of a number of categories that we are using.