Cohomology of Small Cartesian Closed Categories
Category Theory
2025-12-10 v2
Abstract
We show the isomorphism between the Quillen cohomology and the Baues-Wirsching cohomology of a cartesian closed category (CCC). This is an extension of the results of Dwyer-Kan for small categories and Jibladze-Pirashvili for small categories with finite products. These results implies that The Quillen cohomology of a CCC C coincides with that of C as a category with finite products, and also that of C as a small category
Keywords
Cite
@article{arxiv.2510.00488,
title = {Cohomology of Small Cartesian Closed Categories},
author = {Mirai Ikebuchi},
journal= {arXiv preprint arXiv:2510.00488},
year = {2025}
}