John GoodrickByunghan KimAlexei Kolesnikov2026-03-222026-03-22201010.48550/arxiv.1006.4410https://doi.org/10.48550/arxiv.1006.4410https://andeanlibrary.org/handle/123456789/83780Citaciones: 1This paper continues the study of generalized amalgamation properties. Part of the paper provides a finer analysis of the groupoids that arise from failure of 3-uniqueness in a stable theory. We show that such groupoids must be abelian and link the binding group of the groupoids to a certain automorphism group of the monster model, showing that the group must be abelian as well. We also study connections between n-existence and n-uniqueness properties for various "dimensions" n in the wider context of simple theories. We introduce a family of weaker existence and uniqueness properties. Many of these properties did appear in the literature before; we give a category-theoretic formulation and study them systematically. Finally, we give examples of first-order simple unstable theories showing, in particular, that there is no straightforward generalization of the groupoid construction in an unstable context.enUniquenessSimple (philosophy)MathematicsGeneralizationFunctorAbelian groupGroup (periodic table)Context (archaeology)AutomorphismPure mathematicspreprint