DEF0003canonicalv1Progression Operator rho
The sole ontic operator rho: acts as successor within each orbit ray. No other operation creates objects.
Payload
Progression Operator rho
The sole ontic operator rho: acts as successor within each orbit ray. No other operation creates objects.
Progression Operator rho
Summary
The sole ontic operator rho: acts as successor within each orbit ray. No other operation creates objects.
Statement
\label{def:progression}
The \textbf{progression operator} $\rho : \Obj(\tau) \to \Obj(\tau)$
is the unique unary function symbol in $\Sigma_\tau$.
For each object $x$, $\rho(x)$ is called the \textbf{successor} of~$x$.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-01.jsonlline 3 - Manuscript source:
2nd-edition/book-i-categorical-foundations/02_mainmatter/part01/ch02-rho-omega.texlines 43-48
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookI.Kernel.Axioms - Name:
Tau.Kernel.rho
Dependencies
- Canonical: I.D01
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.D02progression-operator-rhodef:progressionRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
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.