IndisputableMonolith.Foundation.UniversalForcing.CategoricalRealization
This module supplies the canonical categorical realization of the Peano object inside the LogicNat algebra for the Universal Forcing program. Workers on invariance and axiom audit results cite it to anchor the natural-number object in categorical terms. The module consists of one import from CategoricalLogicRealization together with the exposed realization definition.
claimThe canonical categorical realization of the Peano natural-number object via the LogicNat algebra, $R : C(L) $ where $L$ denotes the initial Peano algebra.
background
The module lives inside the Foundation.UniversalForcing layer and imports CategoricalLogicRealization. That upstream module packages the natural-number object idea in the same initial-Peano-algebra language used by ArithmeticOf, without rebuilding category theory. The local doc comment identifies the content as the canonical categorical realization via the LogicNat Peano object.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds AxiomAudit, which supplies the reproducible theorem surface, and the Universal invariance theorem stating that every Law-of-Logic realization carries canonically equivalent forced arithmetic. It therefore supplies the categorical hook required by the Universal Forcing chain.
scope and limits
- Does not rebuild category theory foundations.
- Does not prove arithmetic identities directly.
- Does not extend beyond the Peano object realization.
- Does not address forcing steps outside the categorical layer.