Sethood of AcSetA in the Token Space construction

Determine whether the collection AcSetA, introduced to define the subset U ⊆ Set used in constructing the Token Space TS = SX M(U(-) (Set × U)), constitutes a set within the category Set under the framework adopted in the paper.

Background

In Section 4.1, the Token Space TS is defined using a subset U of Set, written as U = AcSetA. The authors immediately raise a foundational question about whether AcSetA itself is a set, highlighting limitations in enumerating all sets in Set and proposing to work with a practically known subset U.

Clarifying the sethood of AcSetA is necessary to formally ground the Token Space construction, since TS is built from SX M(U(-) (Set × U)). Establishing whether AcSetA is a set would ensure categorical well-definedness of the framework.