This paper shows a new phenomenon in higher cluster tilting theory. For each positive integer d, we exhibit a triangulated category
𝖢 with the following properties.
On the one hand, the d-cluster tilting subcategories of 𝖢 have
very simple mutation behaviour: Each indecomposable object has
exactly d mutations. On the other hand, the weakly d-cluster
tilting subcategories of 𝖢 which lack functorial finiteness can
have much more complicated mutation behaviour: For each 0 ≤ ℓ
≤ d - 1, we show a weakly d-cluster tilting subcategory
which has an indecomposable object with precisely
The category 𝖢 is the algebraic triangulated category generated
by a (d + 1)-spherical object and can be thought of as a higher
cluster category of Dynkin type A∞.