In the following recent talk Laurent Lafforgue gives a beautiful overview of the role of categories in Grothendieck’s work and a presentation of some recent developments involving toposes:
Around toposes
A blog and forum about toposes, 'bridges' and the unification programme.
An amazing point of view…
Laurent exhibits razor blade frankness .. but he can afford it …..
Thanks, it was a great talk.
i was wondering about the categorification of Galois theory, namely the equivalence between the covers of an object S and the category of G-set. In fact, i know it’s possible to obtain a von Neumann algebra from an action of group. That’s why i’m asking for a categorification of some operator algebras, if this makes sense.