Cartesian closed varieties (part 3)

Richard Garner – 11 November 2020

In the previous talk in this series, I characterised the category of (non-degenerate) finitary cartesian closed varieties as being equivalent to the category of (non-degenerate) Boolean restriction monoids.

In this final part, I explain how to drop the assumption of finitariness, and show that (non-degenerate) cartesian closed varieties correspond to (non-degenerate) strongly zero-dimensional join restriction monoids. If I have time, I will also explain how models of a cartesian closed theory relate to sheaves on the associated restriction monoid.