A Conceptual Tower of Mathematical Structures: From Sets to Meta-Frameworks

This paper proposes a structured overview of core mathematical structures, arranged in a conceptual tower from foundational to meta-theoretical frameworks. The classification aims to illuminate the relationships between key domains in mathematics, such as algebra, topology, geometry, analysis, and category theory. Emphasis is placed on the increasing levels of structural richness, abstraction, and applicability, with a view toward foundational clarity and unification.Note: There is a small typo — Riemannian manifold is listed under Geometric Structures, when it should be under the Manifold level. This will be corrected in future versions. Also, the natural place of manifold is after topology and before geometry.