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arXiv · 2510.00488

Cohomology of Small Cartesian Closed Categories

Mirai Ikebuchi
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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

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Mirai Ikebuchi. 2025-12-09. Cohomology of Small Cartesian Closed Categories. https://arxiv.org/abs/2510.00488

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