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Lie's Third Theorem in Synthetic Differential Geometry

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If you have a question about this talk, please contact Tamara von Glehn.

This talk will describe a generalisation of Lie’s third theorem in which Lie groups are replaced by a special type of category. The local approximation of such a category will be constructed using an intuitionistic double negation operation. First we will review the classical Lie correspondence and recall the definition of the germ of a local Lie group. Then we will discuss a few attempts to generalise Lie’s third theorem by considering different approximation procedures and working in different ambient categories. Finally we will sketch a proof of Lie’s third theorem using the double negation approximation procedure and the theory of synthetic differential geometry.

This talk is part of the Category Theory Seminar series.

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