adhesive non-collapse

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Editorial synthesis · provisional

Definition

Adhesive non-collapse is the manuscript’s use of a gluing theorem: in an adhesive category, a pushout joining two becomings along a monic interface preserves their embeddings. Iterated tree-like attachment along such interfaces supports non-collapse under the stated conditions. Local monic seams do not guarantee every global composition remains injective; cyclic identifications can collapse distinctions even when each separate interface is monic.

Explanation

The regime model calls collapse the failure of a colimit coprojection to be monic: distinct states of a participating becoming become identified in the composed world. Weak compossibility requires a colimit with monic coprojections. The adhesive construction supplies a sufficient gluing pattern, not a claim that all diagrams satisfy that requirement.

The source restricts its iterated argument to tree-like attachment along a single monic interface at each step. Its Set counterexample identifies two different elements of one participant with the same element of another through two interfaces. The global quotient then collapses the first participant despite the individually monic seams, making the coherence qualification essential.

Non-collapse is itself weaker than the ethical condition the manuscript wants. A world can retain distinguishable components while making their possible revisions inert. Preserved exits are added separately in strong compossibility, and the author identifies this formalization as a modeling choice whose normative force comes from ethics rather than category theory alone.

Scope and attribution

Retain the sufficient-condition theorem with its counterexample and avoid automatic ethical certification.

PB — The Possible Book

The theorem’s two-part and tree-like hypotheses differ from arbitrary cyclic gluing and from strong compossibility.

Occurrence locators: 175, 176, 177, 178, 179, 180, 181.

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.