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Smooth Infinitesimal Analysis III

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

This will be the last talk on Smooth Infinitesimal Analysis. With Fubini’s theorem we will conclude the reformulation of classical analysis within SDG using just the Kock-Lawvere and Integration axiom and move on to some further important concepts: the infinitesimal neighborhoods of the diagonal and the Fermat-Reyes axiom. We will prove the Fermat-Reyes axiom from the integration axiom. Using Fermat-Reyes we will show R^n reflexive. (This will be of importance for later results, since reflexivity is an algebraic reformulation of paracompactness of smooth manifolds.)

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

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