Non-commutative Stone duality: \'etale categories and their monoids.

Thursday 8th December, 2022 16:00-17:00 Maths 311B

It is well-known that there is a relationship between pseudogroups and \'etale groupoids,

where we think of \'etale groupoids as being non-commutative topological spaces.

However, groupoids are equipped with an involution which is important in getting C*-algebras

but is unnatural from the point of view of topological spaces.

In this talk, I shall define what is meant by an \'etale topological category and show that

just as with \'etale groupoids there is an associated monoid and that, in this way we obtain a duality theory.

This is joint work with Ganna Kudryavtseva which appeared in 2017 in Advances in Mathematics:

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