The Maximality of Cartesian Categories
Kosta Dosen, Zoran Petric
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.
Create a lesson
Related papers
Failure of Higher-Order Truth within Intuitionistic Propositional Logic
Lingyuan Ye, Yiqi Xu
Finitistic dimensions in triangulated categories with a compact silting generator
Xiaoyan Yang
De Morgan's Laws in Tensor-Triangular Geometry
Mark Lyttle
Absolute colimits
Richard Garner, Ross Street
A Categorical Framework for the Direct Integration of Banach Spaces
Daniel Funck, Giacomo Gavelli
The Cofree Functor on G-Sets and Its Approximations
Frank Murphy-Hernandez