Let \(\mathscr {C}\) be a 2-Calabi–Yau triangulated category with two cluster tilting subcategories \(\mathscr {T}\) and \(\mathscr {U}\). A result from Jørgensen and Yakimov (Sel Math (NS) 26:71–90, 2020) and Demonet et al. (Int Math Res Not 2019:852–892, 2017) known as tropical duality says that the index with respect to \(\mathscr {T}\) provides an isomorphism between the split Grothendieck groups of \(\mathscr {U}\) and \(\mathscr {T}\). We also have the notion of c-vectors, which using tropical duality have been proven to have sign coherence, and to be recoverable as dimension vectors of modules in a module category. The notion of triangulated categories extends to the notion of \((d+2)\)-angulated categories. Using a higher analogue of cluster tilting objects, this paper generalises tropical duality to higher dimensions. This implies that these basic cluster tilting objects have the same number of indecomposable summands. It also proves that under conditions of mutability, c-vectors in the \((d+2)\)-angulated case have sign coherence, and shows formulae for their computation. Finally, it proves that under the condition of mutability, the c-vectors are recoverable as dimension vectors of modules in a module category.

令\（\ mathscr {C} \）为具有两个簇倾斜子类别\（\ mathscr {T} \）和\（\ mathscr {U} \）的2-Calabi–Yau三角分类。Jørgensen和Yakimov（Sel Math（NS）26：71–90，2020）和Demonet等人的结果。（Int Math Res Not 2019：852–892，2017）称为热带对偶性，它表示关于\（\ mathscr {T} \）的索引在\（\ mathscr {U} \ ）和\（\ mathscr {T} \）。我们也有c的概念使用热带对偶的向量已被证明具有符号一致性，并且可以作为模块类别中的模块的维向量进行恢复。三角分类的概念扩展到\（（d + 2）\）三角分类的概念。使用簇倾斜物体的更高模拟，本文将热带对偶概括为更高维度。这意味着这些基本的群集倾斜对象具有相同数量的不可分解的求和项。还证明了在可变条件下，\（（d + 2）\）成角的情况下的c向量具有符号相干性，并给出了计算公式。最后，它证明了可变性的情况下，下Ç-vector可作为模块类别中模块的尺寸向量恢复。