In computer science there is a term "refinement". Refinement is a hierarchical relationship between two concepts. If B refines A, then the requirements of B are a superset of the requirements of A. Thus, the set of abstractions that model B are a subset of those that model A, i.e., every B is an A.
At the same time there is a term "lifting". It stands for finding a concept with least requirements to fit a particular algorithm.
The question is how to describe A in terms of B if B is a refinement of "A". Similar to ancestor vs. descendant.
My guess is "A is a lifting of B". But I'm not sure I can use "a lifting" in English.