Editing Openai/696eca7b-acdc-800a-9ad9-5ebc9f477576 (section)

==== 2) Make it less trivial: separate “kinds of change” with generators ====

The thin-category above collapses which process occurred. If you want “hypertrophy vs satellite fusion vs epigenetic shift” to be distinguishable, define a free category from a graph of primitive steps.

===== Definition (generated category) =====

Objects: the same triples M=(n,e,c)M=(n,e,c)M=(n,e,c).

Generate morphisms by three primitive “moves” whenever they stay in N3\mathbb N^3N3:
* h:(n,e,c)→(n,e,c+1)h: (n,e,c)\to (n,e,c+1)h:(n,e,c)→(n,e,c+1)  (hypertrophy increment)
* s:(n,e,c)→(n+1,e,c)s: (n,e,c)\to (n+1,e,c)s:(n,e,c)→(n+1,e,c)  (satellite fusion increment)
* p:(n,e,c)→(n,e+1,c)p: (n,e,c)\to (n,e+1,c)p:(n,e,c)→(n,e+1,c)  (priming / expression readiness increment)

Then morphisms are finite strings of h,s,ph,s,ph,s,p (and identities), with composition by concatenation.

Now you can ask: do these moves commute? Not always—so you can add relations.

===== Optional relations (to encode biology-ish constraints) =====

For example, “capacity increases are limited without enough nuclei”:
* impose that hhh is only allowed when c≤k⋅nc \le k\cdot nc≤k⋅n (a myonuclear-domain style constraint)

That’s not category theory per se; it’s just a constraint on when generators exist.