category Directory Reference

Directory dependency graph for category:

Files
	action.cppm
	The Morphisms of Influence (Actions and Representations).
	adjunction.cppm
	Adjoint functors (the Free / Forgetful axis).
	automaton.cppm
	The matcher of a set of words of one length, specialised to it: the minimal automaton of \(\Sigma^* L\), a value computed by one constexpr function at either binding time.
	cartesian.cppm
	Cartesian Closed Category (CCC) Foundations.
	cartesian_bicategory.cppm
	The meet is the right adjoint of the diagonal (Δ⊣∧), reified.
	category.cppm
	Level 0–4: categorical bedrock + ETCS facade.
	chain.cppm
	Dedekind's chain as a range: the unfold of a seed by a coalgebra, the chain of a step guarded by an end, the arrow mapped along it, the bounded chain [lo, hi], and the default chain of a carrier with the NNO's step (the Jlt paper's Figure 2 and Listing 3, #981). The NNO itself, its step and Lambek's destructor Prior, are :nno's; the folds over a chain are :total's concat and :action's fold.
	comprehension.cppm
	Monad comprehensions over a finite chain: the queries of SQL and LINQ, where, select, order_by and take, and the folds that end them.
	concrete.cppm
	Concrete categories: faithful U : 𝒞 → Set, sub-object machinery, lattice operations on χ-classified sets.
	discrete.cppm
	The Discrete Infrastructure (Points as Arrows).
	equivalence.cppm
	Equivalence relations: reflexive + symmetric + transitive predicates, composing the existing axiom traits in :species with a new symmetry trait.
	etcs.cppm
	Elementary Theory of the Category of Sets (ETCS) facade.
	f_algebra.cppm
	Initial F-algebras and terminal F-coalgebras.
	factorisation.cppm
	(Regular epi, mono) factorisation system theory — the categorical context for the image-as-coequalizer-of-kernel-pair theorem narrated in :image (#718 Slice 1).
	filtered.cppm
	Filtered categories — categories whose finite diagrams have a cocone.
	functor.cppm
	The Functorial Spine (Structure Preservation).
	image.cppm
	Image-as-coequalizer-of-kernel-pair: IsImageOf<S, F> on the mono side and IsCoequalizer<Q, F, G> on the quotient side.
	involution.cppm
	Involution — a direction-reversal that is its own inverse — the atomic shape behind the dagger of a \(\dagger\)-category.
	iso.cppm
	The retract / iso-enabling arrow surface: the constructions that turn a factorisation class into a downstream decidability class.
	kleisli.cppm
	The Kleisli Partition (The Extension Systems).
	lattice.cppm
	Lattice categories — the Form-chain row 4 (#698).
	lattice_term.cppm
	The assembled lattice-law term reducer: the normal form of a term over a bounded lattice, built from the induced laws in :lattice, as one algebra for cata, its type at compile time and its value at run time.
	limit.cppm
	Universal Limits: boundary objects (Initial and Terminal) and binary products.
	logic.cppm
	The Rules of Thought (Ω).
	mereology.cppm
	Embryonic Mereology (Part-Whole and Skew Algebraic Core).
	monad.cppm
	Monads and Comonads (Context as Algebra).
	morphism.cppm
	The Skeletal Morphism (Structural Cement).
	natural.cppm
	Natural Transformations (The Slide between Functors).
	nno.cppm
	The Natural Numbers Object — Lawvere's ETCS Axiom 9 — and the upstream home of Peano recursion / primitive recursion / the Peano successor (categorical idiom + textbook synonyms below).
	numeric.cppm
	The Numeric Landing (IEEE 754 and Lipschitz Boundaries).
	partial.cppm
	The Logic of Potentiality (Partial Algebra).
	periodic.cppm
	Periodic arrows on the counts and the counts they license: an arrow f is periodic with period p when \(f(k + p) = f(k)\), a law declared at a generator and inferred at a composite, so that a count along a chain of any length is (n div p) periods and a remainder (the Jlt paper's tensor exhibit, #1104).
	posetal.cppm
	Posetal categories — categories derived from partial orders.
	pullback.cppm
	Limits — Equalizers and Fiber Products (Pullbacks).
	runs.cppm
	Run lists over a finite chain: a subset of \([0, n)\) as the positions where its membership changes, the canonical form of a decidable set on a chain, bounded by its type and on the stack.
	small.cppm
	Small Categories (Enumerated Morphism Sets).
	species.cppm
	The Reified Machine (The Taxonomic Bricks).
	thin.cppm
	Thin categories — categories whose hom-sets contain at most one morphism.
	topoi.cppm
	The Internal Logic of the Topos.
	total.cppm
	The Laws of Total Algebra (The Algebraic Hierarchy).