Oxford Seminar / Hyperdoctrines in DOTS
Description
In this talk we motivate and define (regular) hyperdoctrines and sketch how to view them as double-operadic systems theories. We relate this to the notion of systems with certificates, which allows us to formally verify a systems theory’s properties in a way that is reminiscent of the internal language of a category. Finally, we sketch a program to generalise this procedure to other logics (and functorialise it), and express some of the benefits of this program for strengthening the toolbox of categorical systems theory.
Assumed knowledge: General category theory, especially monoidal categories, double categories and adjunctions. Familiarity with functorial semantics and/or DOTS would help but isn’t necessary.