University of Cambridge > Talks.cam > Synthetic Differential Geometry Seminar > The Kock-Wraith axiom schema and Microlinearity

The Kock-Wraith axiom schema and Microlinearity

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If you have a question about this talk, please contact Filip Bár.

Until now we have encountered with various kinds of notions of infinitesimals. In this talk we will develop a systematic approach towards a general notion of infinitesimals using Weil algebras. This will enable us to generalize the K-L axiom to the Kock-Wraith axiom schema and to give the definition of a microlinear space. The category of microlinear spaces is a Cartesian closed full subcategory of our smooth universe closed under all small limits. Moreover, the category of microlinear spaces provides a very general and very convenient framework for the geometry of infinitesimals, which we will develop in the next talks beginning with tangent vectors and the tangent bundle.

This talk is part of the Synthetic Differential Geometry Seminar series.

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