Closure under inverse is like the most important idea in math, physics and probability. Linear logic, constructive math, probability, quantum mechanics all have

Closure under inverse is like the most important idea in math, physics and probability. Linear logic, constructive math, probability, quantum mechanics all have in common that they rely on closure under adjoint and norm which in turn give you closure under inverse. I wrote something on the topic but it's very incomplete https://github.com/adamnemecek/adjoint https://github.com/adamnemecek/adjoint