Yılmaz, Deniz2025-02-212025-02-212024-120022-4049https://hdl.handle.net/11693/116599Let k be an algebraically closed field of characteristic p > 0 and let F be an algebraically closed field of characteristic 0. Recently, together with Bouc, we introduced the notion of functorial equivalences between blocks of finite groups and proved that given a p -group D , there is only a finite number of pairs ( G, b ) of a finite group G and a block b of kG with defect groups isomorphic to D , up to functorial equivalence over F. In this paper, we classify the functorial equivalence classes over F of blocks with cyclic defect groups and 2 -blocks of defects 2 and 3. In particular, we prove that for all these blocks, the functorial equivalence classes depend only on the fusion system of the block.EnglishCC BY-NC-ND 4.0 DEED (Attribution-NonCommercial-NoDerivatives 4.0 International)https://creativecommons.org/licenses/by-nc-nd/4.0/deed.enBlockFunctorial equivalenceFusion systemSplendid Rickard equivalenceArticle10.1016/j.jpaa.2024.1077441873-1376