The formalization of what it means for modules to exist and compose with each other is valuable, but learning category theory as a mathematician would is not su

The formalization of what it means for modules to exist and compose with each other is valuable, but learning category theory as a mathematician would is not sufficient for grokking this. Category theory's insights are often obscured by terminology that fails to reify the abstractions at a level where its wide scope becomes clear. The candidate I would push forward as the proper reification would be Mark Burgess' Promise Theory. Mark's starting point isn't, "what's the most general algebra I can form for encoding mathematical objects", but "what happens if I generalize points in spacetime to be a special case of any kind of graph". When you do this, you make each point in space responsible for either promising information to another point, or accepting the outcome of a promise, as bidirectionality cannot be directly inferred. So if every point in spacetime cannot be assumed to be connected both ways, then you have to explicitly define the communication channels that exist between points. This idea unifies both physical and digital "spaces", as everything is now modeled as a communications network from atoms up. Thus, Promise Theory makes the connection between compositionality and information and the rest of reality more clear than categories alone. Mark acknowledges that Category Theory and Promise Theory are both similar and related. For instance, they both deal with notions of interiority. And Mark encodes his axioms with categories. He's written several books on the topic, like "In Search of Certainty" and "Smart Spacetime", and has published papers on arxiv. I recommend "Smart Spacetime" to see how powerful this kind of semantics can get. https://arxiv.org/abs/1411.5563 https://arxiv.org/abs/1411.5563