Further reading

Gold’s identification-in-the-limit paradigm supplies the presentation and convergence discipline underlying UOCL [ Gold , 1967 ] . The Grothendieck construction and indexed-category viewpoint are reviewed in Chapter 1. Lawvere’s functorial semantics, Ehresmann sketches, and PROPs supply the theory-bearing refinement [ Lawvere , 1963 , Ehresmann , 1968 , Lack , 2004 ] . Piaget motivates the operational separation of assimilation and accommodation [ Piaget , 1952 ] , while universal imitation games supply the coinductive special case in which behavioral prediction, rather than categorical reconstruction, is the target [ Mahadevan , 2024 ] . The category \(\mathsf{Learn}\), the \((P,I,U,r)\) interface, and the symmetric monoidal composition of supervised learners are developed by Fong et al. [ 2019 ] ; their construction is the direct prototype for the open UOCL interface introduced here.