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The Maximality of Cartesian Categories

1999/11/10 by Kosta Došen, Kosta Dosen, Dosen, Kosta +3
Computer Science · Mathematics · #03G30 (Secondary) #18A30 (Primary) 18A15 #Category Theory (math.CT) #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #math.CT #math.LO #msc:03G30 #msc:18A15 #msc:18A30

paper · pdf · doi:10.48550/arxiv.math/9911059

8 pages

arxiv created 1999/11/10 · openalex publication_date 1999/11/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that equalities between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equality in the language of free cartesian categories collapses a cartesian category into a preorder. An analogous result holds for categories with binary products, which may lack a terminal object. The proof is based on a coherence result for cartesian categories, which is related to model-theoretical methods of normalization.

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