Gabriele Lobbia (Università di Bologna) will give a talk on
Sketches and Classifying Logoi
Abstract:
The notion of sketch, introduced by Ehrensmann, has been considered as one of the many formalisation of the concept of theory. In particular, it can be used to present theories in infinitary logics.
In this talk I will show how we used sketches to extend what was done with sites and topoi in the context of geometric logic to infinitary logic. More precisely, we want to replicate the pattern that sites are presentations of geometric theories and that the classifying topos gives a syntax independent avatar of the theory.
In the first part of the talk I will show some nice (topological) properties of the 2-category of sketches, which turn out to be useful for some important constructions. For instance, we give an explicit formula to calculate weighted pseudo co/limits in the 2-category of sketches and we prove that the tensor product for sketches (studied by Benson) is closed.
Then, I will provide some normalisation constructions which will be useful for our main result: a Diaconescu-like theorem for our notion of presentations (rounded sketches) and syntax independet objects (logoi).
This talk is based on joint work with Ivan Di Liberti.