In Aggrotopy Type Theory (ATT) the specific forcing operation for lifting one type onto another is not explicitly defined. However, we can speculate on a hypothetical basic forcing operation that could be used in ATT to lift or transfer one type onto another.
In this speculative description, the basic forcing operation in ATT could involve the following steps:
Given two types, let's call them Type A and Type B, where we want to lift Type A onto Type B.
The forcing operation starts by defining a function, let's call it lift, which takes an element from Type A and maps it to an element of Type B. This function establishes the relationship between the two types.
The lift function would typically involve a mapping or transformation process that preserves the structure or properties of the elements being lifted. It ensures that the lifted elements in Type B maintain certain characteristics inherited from their corresponding elements in Type A.
The forcing operation may include additional constraints or conditions that specify how the lifting should be performed. These constraints could depend on the specific properties or relationships between Type A and Type B, ensuring that the lifting operation preserves certain desired features or satisfies certain criteria.
The resulting lifted type, which is Type B with elements lifted from Type A, inherits the structure, properties, and relationships defined by the forcing operation.
It's important to note that this description is speculative and does not represent a formal or established forcing operation within ATT or any specific type theory. The actual forcing operation in ATT would require a well-defined set of axioms, rules, and principles that determine the process of lifting one type onto another.