All Concepts are $\mathbb{C}\mathbf{at}^\#$
Abstract
We show that the double category of comonoids in the category of polynomial functors (previously shown by Ahman-Uustalu and Garner to be equivalent to the double category of categories, cofunctors, and prafunctors) contains several formal settings for basic category theory and has subcategories equivalent to both the double category of dynamic rewiring systems and the double category of generalized polynomials in a finite limit category . Also serving as a natural setting for categorical database theory and generalized higher category theory, at once hosts models of a wide range of concepts from the theory and applications of polynomial functors and category theory.
Cite
@article{arxiv.2305.02571,
title = {All Concepts are $\mathbb{C}\mathbf{at}^\#$},
author = {Owen Lynch and Brandon T. Shapiro and David I. Spivak},
journal= {arXiv preprint arXiv:2305.02571},
year = {2024}
}
Comments
31 pages. Proofs in appendix moved into the main body, and chapter on nerves of higher categories removed to a separate submission at arXiv:2405.13157