Thoughts on bifibration as gesture

A quick note so I don’t forget. In the ‘Philosophy of Gesture’, Maddalena defines a gesture as being a sign where the iconic, indexical, and symbolic elements are particularly well defined. Mellies work proposes the bifibration as a key component to his new existential graphs. Fibrations have a lifting property, while opfibrations have an extension property. Thus, a bifibration is simultaneously a functor (compositional), an extension and a lift. It is therefore a candidate for a mathematical model of a gesture, as well as being a key notion in the new existential graphs.

Also, Mellies states that his work builds upon Hermida’s thesis. I’m not sure how yet. I thought Hermida’s ‘relational parametricity’ research program was aligned with Maddalena’s definition of synthetic inference as maintaining identity through changes. Atkey’s work on Noether’s theorem would be a good example of such.