AXM0008canonicalv1Object Closure (K6)
Obj(tau) = {omega} union O_alpha union O_pi union O_gamma union O_eta; no other objects exist.
Payload
Object Closure (K6)
Obj(tau) = {omega} union O_alpha union O_pi union O_gamma union O_eta; no other objects exist.
Object Closure (K6)
Summary
Obj(tau) = {omega} union O_alpha union O_pi union O_gamma union O_eta; no other objects exist.
Statement
%
\label{ax:object-closure}
Every object of $\tau$ belongs to one of the five canonical sets:
\[
\boxed{%
\Obj(\tau) = \{\omega\}
\;\cup\; O_\alpha
\;\cup\; O_\pi
\;\cup\; O_\gamma
\;\cup\; O_\eta.
}
\]
No object exists outside these five sets.
Proof / Justification
This item is an axiom. No manuscript proof is required.
Source Context
- Registry source:
book-01.jsonlline 11 - Manuscript source:
2nd-edition/book-i-categorical-foundations/02_mainmatter/part01/ch04-closure-tau-zero.texlines 49-63
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookI.Kernel.Axioms - Name:
Tau.Kernel.K6_object_closure
Dependencies
- Canonical: I.D01, I.D02
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
I.K6object-closure-k6ax:object-closureRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (1)
Appears in (1)
Downstream uses (computed) (2)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
Sources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.