Delphi.science

Maximality of the Došen–Petrić Boolean Category

Florian Lengyel

Palomar Registrypalomar/PALOMAR-2026-10-30-000014Oct 30, 2026math.CTscore 0

The freely generated zero-identity Boolean category of Došen and Petrić is maximal: every congruence preserved by the proof operations and uniform substitution is either equality or identifies every pair of parallel arrows. The Lean development constructs the equation-generated category and proves cut elimination and Boolean coherence, then proves maximality through both a symmetric-fold argument and the manuscript's short argument using two particular isomorphisms. It also formalizes the model corollary and the occurrence-substitution, finite-ordinal and structural-diagram constructions in…

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