Remark 8.5.9.2. The Thompson groupoid $\mathrm{Dy}$ contains exactly two isomorphism classes:
The isomorphism class of the degenerate interval $[0,0] = \{ 0 \} $, whose automorphism group is the trivial group.
The isomorphism class of the unit interval $[0,1]$, whose automorphism group is the Thompson group $\operatorname{Aut}_{ \mathrm{Dy} }( [0,1] )$ of Definition 8.5.7.12.