[P3] ================================================ AMAST Links 02 06

                   Question about Generalised Spaces

  I have the following question : can the adjunction between
topological spaces and locales be lifted to an adjunction between
Generalised Spaces and Grothendieck toposes. I.e. we are looking for

   locales:spaces  =  Groth. toposes:?  (*)

  Clearly, for any Grothendieck topos E the category of points of E is
an accessible category. But if A is an accesible category then the
accessible functors to Set are the preshaeves over A_pres the category
of presentable objects of A (surely one has to fix a cardina, say
alpha_0).  So things don't work so easily.

  I mean there is already a problem that (*) does not specify the ?
(generalised spaces) uniquely.

  So my question is whether there is a notion of accessible category +
some further conditions which is an appropriate fill-in for ? in (*).

  Maybe the answer is well-known but I simply couldn't find it easily
in the literature.

  Thomas Streicher