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Categorical & Representation-Theoretic Structures

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Abstractions about algebraic structures built from categorical and representation-theoretic constructions, covering tensor and module structures (Bimodule, Exterior Algebra, Associativity Isomorphism), representation theory (Character Theory, Fusion Category), and combinatorial or group-theoretic constructs like the Baxter Permutation and Sastry Automorphism.

8 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

  • Associativity Isomorphism — A natural family of isomorphisms rebracketing a categorical tensor product, constrained by the pentagon coherence identity.
  • Baxter Permutation — A finite permutation avoiding the adjacency-sensitive patterns 2-41-3 and 3-14-2, forming an enumerated family with recursive, planar, tree, rectangulation, and algebraic representations.
  • Bimodule — An abelian group with a left action by one ring and a right action by another that commute, so applying the two actions in either compatible order gives the same result.
  • Character Theory — The study of group representations through trace-valued class functions whose orthogonality and arithmetic encode irreducible decomposition and group structure.
  • Composition Algebra — A unital algebra with a nondegenerate quadratic form whose value is multiplicative under the algebra product.
  • Exterior Algebra — Turn alternating multilinear combinations of a module into ordinary linear algebra by quotienting its tensor algebra so every repeated degree-one factor vanishes, producing a graded wedge product with a universal mapping property.
  • Fusion Category — Model finitely many particle-like object types with semisimple direct-sum decomposition, duals, and an associative tensor product whose decomposition coefficients form finite fusion rules.
  • Sastry Automorphism — A characteristic-two field automorphism admitting a nonzero quadruple that satisfies the Type I or Type II Sastry–Bombieri identity system arising from Ree-group embeddings in F4.