Generic representations of orthogonal groups: The functor category image

In this paper, we define the functor category image associated to image-vector spaces equipped with a quadratic form. We show the existence of a fully faithful, exact functor image, which preserves simple objects, where image is the category of functors from the category of finite-dimensional image-vector spaces to the category of all image-vector spaces. We define the subcategory image of image, which is equivalent to the product of the categories of modules over the orthogonal groups; the inclusion is a fully faithful functor image which preserves simple objects.