Элементарные ротации операторов в категориях с квадратичным расширением

Some classes of inner spaces and operators in them are studied from the point of view of category theory. Notions of matrix category and category with quadratic decomposition are introduced. The category of all nondegenerated spaces and the category of all Krein spaces are special cases of above-mentioned categories. The definition of elementary rotation (or Julia operator) well-know in Krein spaces operator theory are generalized for the case of arbitrary matrix category. the main result of this paper is proof of existing for an arbitrary operator from category with quadratic decomposition of elementary rotation from the same category.