categorical colimit

Compiled with AI assistance and selectively reviewed. Please consult the cited passages; the books remain the authoritative source. About this companion

Editorial synthesis · provisional

Definition

A categorical colimit is the universal cocone of a diagram: the freest joint realization through which every other cocone factors uniquely. The manuscript uses this construction to articulate relational organization and accumulated actualization. It distinguishes computing such a universal object from the actual taking of one admissible cocone, so the construction supplies comparisons among possible worlds rather than a mechanism selecting the world that occurs.

Explanation

The regime module presents a diagram of participating becomings and its cocones as possible composed worlds. The colimit is initial among these cocones, giving a unique comparison into each. In the jointly epic case that comparison has a quotient-like role. This universal property organizes the proposed formal account; it does not measure ethical goodness.

The earlier scaffold says individuation takes one admissible cocone rather than simply computing the colimit. It also marks the multiplicity-principle formulation as unverified. Formal availability consequently does not explain why a particular compatible realization occurs, nor establish that the philosophical identification with ontic novelty is forced by category theory.

The later non-collapse discussion asks whether the colimit’s coprojections preserve distinct states. A universal object can still identify states, so existence alone is weaker than viable coexistence. The proposal keeps this distinction and the ethical module’s warning that its categorical model sharpens an argument without deriving the bindingness of its normative choices.

Scope and attribution

Retain the stated universal property and distinguish mathematical construction from ontic selection.

PB — The Possible Book

The universal cocone, selected world and additional non-collapse conditions remain distinct.

Occurrence locators: 146, 147, 150, 151, 153, 154, 155, 156, 157, 158, 159, 160, 161, 164, 165, 166, 167, 175, 176, 177, 179, 180, 181, 184.

Background used in the editorial explanation

Named theories and mechanisms are distinguished from neighboring background, homonyms and the author’s own synthesis. Reproduced AI passages retain their separate voice.