Mathematical accounting systems are widely used by practitioners to negotiate. For example, stock and flow diagrams account for epidemics and stakeholders use them to negotiate public health policy. Differential equations account for physical laws and scientists use them to hypothesize and run experiments. While these are robust and formal systems, they are siloed. One part of our work at Topos is designing meta-accounting systems — i.e. grammars which house many domain specific grammars. An early example of a meta-grammar is decorated cospan categories (Fong 2015; J. C. Baez, Courser, and Vasilakopoulou 2022) which has been used to define grammars for composing stock and flow diagrams (J. Baez et al. 2023), Hamiltonian and Lagrangian systems (J. C. Baez, Weisbart, and Yassine 2021), and much more.

This is a companion discussion topic for the original entry at https://topos.site/blog/2024-08-12-poly-as-accounting-for-bayesian-update/