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The Tangent Bundle of a Microlinear Space

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

We prove a characterization of quasi colimits, namely that any cone of Weil algebras is a quasi colimit iff R perceives it as a limit (in our smooth universe of sets). This result is of both theoretical and practical relevance. Geometrically it implies that tangent bundle constructions on R, for example, the fiberwise addition of tangent vectors, are universal. Because of this the construction can be transferred to any space that perceives quasi colimits as limits, i.e., it works for the tangent bundle of any microlinear space. In fact, any such tangent bundle turns out to be a K-L vector bundle. (This means that any fiber is a K-L R-module.)

This talk will cover the sections 2.3.2, 3.1, 3.2.1 of Lavendhomme’s book.

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

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