13 August 2020, 18:00, online

Speaker

Robin Cockett, University of Calgary

Title

Fibrations for partial maps

Abstract

Fibrations are a fundamental tool of categorical logic and yet, although computation is fundamentally partial, there is no well-established theory of fibrations for partial settings. Such a theory it would seem should be very useful in the semantics of programming. Indeed, the developments I will be discussing were, in fact, most recently prompted by the desire to gain a full understanding of the semantics of reversible differential programming.

The work is based on the notion of a latent fibration, which was first introduced in Chad Nester's MSc. thesis. Those initial ideas have now undergone a significant development (particularly over the last few months due to the efforts of Geoff Cruttwell, Jonathan Gallagher, and Dorette Pronk). These developments will be the subject of the talk ...