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

=== Define a category 𝓜 as follows. ===

==== Each object is a triple: ====

: 

Where:
* n = number of nuclei
* e = epigenetic state (simplified to an integer scale)
* c = contractile capacity

These are abstract parameters, not biology.

Example objects:
* M₀ = (1, 0, 1) untrained fiber
* M₁ = (2, 1, 3) trained fiber
* M₂ = (3, 2, 5) heavily trained fiber

==== A morphism f : M → M′ is allowed iff: ====
* n′ ≥ n
* e′ ≥ e
* c′ ≥ c

Interpretation: morphisms represent biologically feasible transformations (training, recovery, fusion, adaptation).

So:
* Training gives morphisms upward in all coordinates
* Detraining would not be included unless we explicitly add decay morphisms

This gives us a preorder category (a category generated by a partial order).

Composition is trivial:
If
f : M → M′
g : M′ → M″
then
g ∘ f : M → M″

==== Each object M has an identity: ====

: 

This corresponds to “no change”.

==== - Hypertrophy = morphisms that increase c ====
* Satellite fusion = morphisms that increase n
* Muscle memory = persistence of higher e affecting future reachable morphisms
* DNA invariance = not represented in objects at all → treated as a global invariant parameter of the entire category

This is already a valid mathematical category.

Not metaphorically. Literally.