The category of 3-computads is not cartesian closed
Mihaly Makkai, Marek Zawadowski
TL;DR
This paper proves that the category of 3-computads is not cartesian closed using the Eckmann-Hilton argument, implying that higher computad categories do not form elementary toposes.
Contribution
It demonstrates the non-cartesian-closed nature of 3-computads and higher computad categories, providing a significant insight into their categorical structure.
Findings
Category of 3-computads is not cartesian closed
Categories of all computads and n-computads for n>2 are not elementary toposes
Higher computad categories lack local cartesian closure
Abstract
We show, using Eckmann-Hilton argument, that the category of 3-computads is not cartesian closed. As a corollary we get that neither the category of all computads nor the category of n-computads, for n>2, do form locally cartesian closed categories, and hence elementary toposes.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Logic, programming, and type systems · Computability, Logic, AI Algorithms