2025/10/01 by Mirai Ikebuchi, Ikebuchi, Mirai
Computer Science · Mathematics · #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2510.00488
openalex publication_date 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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