The Maximality of Cartesian Categories

@article{Dosen2001TheMO,
  title={The Maximality of Cartesian Categories},
  author={Kosta Dosen and Zoran Petric},
  journal={Math. Log. Q.},
  year={2001},
  volume={47},
  pages={137-144}
}
It is proved that equations between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equation 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-theoretic methods of normalization. This maximality of cartesian… CONTINUE READING
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