The logical quantization of algebraic groups
These two papers [see also the following one] are a continuation of the work of the author, begun in the papers ``Manuals in orthogonal categories'' [ibid. 34, No. 2, 211-228 (1995; Zbl 0830.18004)] and ``Empirical sets'' [ibid. 34, No. 2, 229-252 (1995; Zbl 0830.18005)]. The author has a program to develop mathematics in a particular categorical setting, which can be viewed as generalizing Boolean topos theory. The starting points are the notions of a manual of Boolean locales and that of an orthogonal category, as well as the concomitant notion of empirical set, which involves the assignment to each Boolean locale in the manual a sheaf over it. Using this general framework, the author looks at algebraic groups and then differential geometry in the spirit of smooth topoi. The intent is that this approach presents the ``quantized'' or ``Booleanized'' versions. It would probably be useful for the reader to first be exposed to the earlier papers where more of the technical details regarding the underpinnings of this theory can be found.
scientific article; zbMATH DE number 792882
scientific article