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A constructive approach to geometric algebra

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If you have a question about this talk, please contact Julia Goedecke.

In classical geometric algebra, we prove that the synthetic and the projective approaches to the affine and projective planes are equivalent. This classical approach is not entirely constructive and it is based on fields.

We will present a constructive version of this based on local rings: we will define what are the projective and affine planes over a given local ring (in a topos), and we will give the geometric theories of projective and affine planes satisfied by these constructions. Moreover, we will show how to construct a local ring given a model of that theory. These constructions induce geometric morphisms between the classifying toposes of the theories of affine and projective planes, and the theory of local rings.

This talk is part of the Category Theory Seminar series.

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