Categorical Algebra & Model Systems¶

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Abstractions about categories, automorphisms, localizing subcategories, representation theory, formal rewriting systems, and model-theoretic rank.

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.

Age (Model Theory) — The isomorphism-closed class of finitely generated structures that embed into a fixed model, recording exactly its finite or finitely generated local patterns.
Auslander–Reiten theory — A representation-theoretic framework organizing indecomposable modules and morphisms through almost-split sequences and Auslander–Reiten quivers.
Automorphism Group — The group obtained by collecting every structure-preserving self-isomorphism of a fixed mathematical object and using composition as the group operation.
Coherent category — Equip a regular category with finite unions of subobjects that remain stable under pullback, providing categorical semantics for finite-limit, existential, and finite-disjunctive reasoning.
Localizing Subcategory — A Serre subcategory whose exact quotient functor admits a right-adjoint section, so the objects it annihilates define a recoverable Gabriel localization of an abelian category.
McKay Graph — Encode tensoring by a fixed finite-group representation as a multiplicity-weighted quiver on irreducible representations, turning fusion rules into adjacency, paths, spectra, and—in the SU(2) case—affine ADE structure.
Post Canonical System — A finite string-production formalism that derives words from finite axioms by matching whole-word antecedent patterns and reassembling their matched variables in consequents.
Regular Category — A finitely complete category in which every morphism has a pullback-stable regular-epimorphism–monomorphism image factorization—equivalently, kernel-pair quotients exist and regular epimorphisms remain regular under pullback.