Epistemological status: Babbling.
Let map each mind in mindspace to how aligned it is. We are trying to optimize . To that end, lemmata are helpful which talk about the shape of mindspace. That's why we try to call it a space even before defining what category it lives in.
To optimize a function, start with a diverse enumeration of its domain. The deontological enumeration covers all others with constant-factor overhead, but the consequentialist enumeration gives us more properties to work with.
Every mind has an implicit utility function . factors through as a function, but not as a continuous function, let alone a -morphism. That's why we've recently moved away from explicit utility maximizers.
Use mathematical language to tell our story! Then we might guess where it's going.