In this short note, we show that the generalized type semigroup W ( X , Γ ) \mathcal {W}(X, \Gamma ) introduced by Ma [Ergodic Theory Dynam. Systems 41 (2021), pp. 2148–2165] belongs to the category W introduced by Antoine, Perera and Theil [Mem. Amer. Math. Soc. 251 (2018), vii+191]. In particular, we demonstrate that W ( X , Γ ) \mathcal {W}(X, \Gamma ) satisfies axioms (W1)–(W4) and (W6). When X X is zero-dimensional, we also establish (W5) for the semigroup. This supports the analogy between the generalized type semigroup and pre-completed Cuntz semigroup W ( ⋅ ) W(\cdot ) for C ∗ C^* -algebras.