English

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}
}