Does the road to categorical semiotics run through Hegel?

Categorical logic, as a mathematical field, is now well established. The relationship between categorical logic and Hegelian logic has been worked out in some detail (although I cannot assess the extent of this detail) by Urs Schrieber. My project is to develop the application of categorical logic (as a mathematical theory) to semiotics (as postmodern philosophy), a project that I have summarized as categorical semiotics (a play on Peirce’s title of “Logic, Considered as Semeiotic”, with the term categorical distributing over the title.

In my early specifications of this project, it looked like the pathway would run through Peirce’s gamma existential graphs. The beta graphs have been extensively investigated through