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Certified naturality and the obstruction to unrestricted naturality in a typed two-dimensional calculus

Arthur F. Ramos

Palomar Registrypalomar/PALOMAR-2026-09-14-000010Sep 14, 2026math.LOscore 0

We formalize the boundary of naturality in the labelled conversion calculus of A Theory of a Two-Dimensional Typed Lambda Calculus. Canonical evaluation of inductively presented homotopies constructs naturality squares, and transport along finite presentations preserves two-paths and recovers the naturality boundary. In contrast, an explicit pointwise family on Fin 3 admits no naturality two-cell or finite pasting: a six-element dihedral-group invariant separates its two boundary paths while respecting every declared two-cell generator. This independently reconstructed refutation is…

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