ScalingStacks

Corollary 3 The only grading-preserving endomorphisms of bimodules ${\mathcal{F}}(\cap_{i,n})$ and ${\mathcal{F}}(\cup_{i,n-1})$ are multiplications by integers. The only grading-preserving automorphisms of bimodules ${\mathcal{F}}(\cap_{i,n})$ and ${\mathcal{F}}(\cup_{i,n-1})$ are $\mathrm{Id}$ and $-\mathrm{Id}.$ Moreover, these bimodules have no graded endomorphisms of negative degree.