University of Cambridge > > Category Theory Seminar > Characterising realisability toposes

Characterising realisability toposes

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Julia Goedecke.

In this talk, I will give a characterisation of realisability toposes over partial combinatory algebras. More precisely, we do not characterise the bare toposes, but the toposes together with the associated ‘constant objects functor’ Delta: Set → RT(A) for a partial combinatory algebra A. By Moens’ theorem, such a functor is equivalent to a fibering of RT(A) over Set (given via glueing).

Our approach is to view realisability toposes as generalised presheaf toposes, where the underlying category is replaced by an underlying fibration. As in the non-fibred case, these generalised presheaf toposes can be characterised in terms of indecomposable projectives. To obtain a characterisation of realisability over a partial combinatory algebra, it remains to characterise the fibrations that are induced by pcas. This is achieved using techniques introduced by Hofstra and Longley in their work on categories of ‘combinatory objects’.

This talk is part of the Category Theory Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2023, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity