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.