Book I · Chapter 69

Chapter 69: Holomorphy as Naturality

Page 315 in the printed volume

Remark [rem:naturality] in Part XIII observed informally that tower coherence is a naturality condition on the primorial category. Part XIV earned the categorical vocabulary — presheaves, natural transformations, functors. This chapter closes the loop: the Presheaf Characterization Theorem (the relevant theorem, I.T40) proves that τ-holomorphic functions are precisely the natural transformations from the primorial presheaf to its split-complex extension that respect the sector decomposition. No topology. No geometry. No analysis. Pure diagram-chasing on finite cyclic groups.