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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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