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On the categorical structure behind Galois theories

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Most realizations of Galois theory rely on a set theoretical Galois group acting by automorphisms of an object in a category. In this talk we will discuss how, if we ask the Galois group to be a group object in the same category that the object in question, then many different incarnations of Galois theory, including classical, Hopf-Galois, differential, and Galois theory adapt to the same categorical framework. We will also see that the realization of such theory in the category of smooth bundles corresponds to some extension of the theory of principal connections in principal bundles. This talk is based on the article “A simplified categorical approach to several Galois theories” in collaboration with C. A. Marín-Arango y J. F. Ruiz.Castrillon. ————————

Meeting ID 993 6591 2480 Passcode 493042 Link https://maths-cam-ac-uk.zoom.us/j/99365912480?pwd=ZE1aNUU4bjdFeVU3azQ1ZHJCSEx0dz09

This talk is part of the Category Theory Seminar series.

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