On a sheaf-theoretic version of the Witt’s decomposition theorem. A Lagrangian perspective

摘要

The approach to a counterpart, in Abstract Geometric Algebra, thatis, Geometric Algebra via sheaves of modules, of the classical Witt’s decomposition theoremis based on the axiomatization of the classical context, which however leads to the formulation of a specific subcategory of the category of sheaves of modules: the full subcategory of convenient sheaves of modules. Convenient sheaves of modules turn out, by the very essence of the matter at hand, to be of further importance as far as the setting of results leading to the sheaf-theoretic aspect of several forms of the Witt’s theorem is concerned.Further versions of the Witt’s theorem are still to be treated elsewhere.