The Maximality of Cartesian Categories

Details The Maximality of Cartesian Categories The Maximality of Cartesian Categories

1999-11-10

arxiv.org/abs/math/9911059v1

Mathematics

Category Theory

8 pages

Scientific paper

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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