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This paper reveals an isomorphism between Quillen and Baues-Wirsching cohomology in categories, implying crucial relationships.
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) studied this question.
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