“…Then Lsc(X, M) is a Cuntz category semigroup whenever X is a second-countable compact Hausdorff space with finite covering dimension and M is countably based (see [4,Theorem 5.17]). It was also shown in [66,Corollary 4.22] that Lsc(X, N) is a Cuntz category object when X is a compact metric space. It was proved in [14,Theorem 10.1] and [38,Theorem 6.11] that Cu(C 0 (X)) ≅ Lsc(X, N), via the rank map, if X is [0, 1] or (0, 1].…”