Category-theoretic graph structures in Rust. The catgraph crate (v0.12.2, slim baseline) is a strict Rust implementation of Fong & Spivak, Hypergraph Categories (2019). Applied-CT extensions (catgraph-applied v0.5.5) track Fong & Spivak, Seven Sketches in Compositionality (2018). Wolfram-physics extensions live in a third workspace crate (catgraph-physics v0.3.0). Magnitude of enriched categories + magnitude homology (catgraph-magnitude v0.3.0) is anchored to Bradley & Vigneaux, Magnitude of Language Models (2025) and Leinster–Shulman, Magnitude homology of enriched categories and metric spaces (2017). Categorical Deep Learning substrate (catgraph-dl v0.3.1) is anchored to Gavranović et al., Categorical Deep Learning is an Algebraic Theory of All Architectures (ICML 2024).
| Crate | Path | Purpose |
|---|---|---|
catgraph v0.12.2 |
catgraph/ |
Strict Fong-Spivak 2019 paper implementation: cospans, spans, Frobenius algebras, hypergraph categories, Theorem 1.2 equivalence, spider theorem (Thm 6.55), Corel<Λ> (F&S 2018 Ex 6.64; v0.12.0), Cospan::compose_with_quotient additive API, parallel feature (WASM + native, W.1). |
catgraph-physics v0.3.0 |
catgraph-physics/ |
Wolfram-physics extensions: hypergraph DPO rewriting, multiway evolution, gauge theory, branchial spectral analysis. |
catgraph-applied v0.5.5 |
catgraph-applied/ |
Applied CT extensions. Tier 1 (v0.3.x): generic DecoratedCospan<F> (Def 6.75, Thm 6.77), Petri nets as hypergraph category, wiring diagrams, E_n operads, Temperley-Lieb, linear combinations. Tier 2 (v0.4.0): props + Free(G) (Def 5.2, 5.25), OperadAlgebra with Circ (Def 6.99, Ex 6.100), OperadFunctor with canonical E₁↪E₂ (Rough Def 6.98). Tier 3 (v0.5.x): Rig + 4 concrete rigs (Def 5.36), SignalFlowGraph<R> (Def 5.45), MatR<R> (Def 5.50), sfg_to_mat functor (Thm 5.53), Presentation<G> with CC decision engine + Layer-1 Joyal-Street NF short-circuit, EnrichedCategory<V> + LawvereMetricSpace<T>, CompleteFunctor<G> + MatrixNFFunctor<R> closing Thm 5.60 semantically (v0.5.2); F64Rig ring + field ops prereq for catgraph-magnitude (v0.5.3); Operadic for WiringDiagram InterCircle: Clone widening (v0.5.4). v0.5.5 (catgraph-magnitude v0.3.0 substrate): mutable MatR<R> row/col API + LawvereMetricSpace::{size, objects, from_distance_fn} + impl From<i64> for F64Rig for in-place Storjohann SNF. |
catgraph-magnitude v0.3.0 |
catgraph-magnitude/ |
Magnitude of enriched categories + magnitude homology. Anchored to BV 2025 + Leinster–Shulman 2017 + Leinster 2013. v0.1.x: Tsallis q-entropy + Shannon recovery + Möbius inversion + LmCategory + WeightedCospan<Λ, Q>. v0.2.x: weighting / coweighting (Leinster 2013 Def 1.1.1) + is_scattered + mobius_function_via_chains (von-Neumann series). v0.3.0: chain_complex over LawvereMetricSpace, integer SNF via Storjohann §7.12 + 2-prime cross-check rank recovery, magnitude_homology_rank<Q> (BV 2025 Prop 3.14 structural path), mobius_chains_graded + is_mobius_invertible_at (numerical Prop 3.14 path), euler_char_identity_at Path C analytical-bound 5-fixture acceptance suite. No tokio, no serde, no rayon. |
catgraph-dl v0.3.1 |
catgraph-dl/ |
Categorical Deep Learning substrate. Anchored to Gavranović et al., ICML 2024 (CDL). Para(M, C) 2-category over (Set, ×, 1) (CDL §3.1) + MonoidalCategory / Actegory<M> / Comonoid<M> traits + DiagonalComonoid weight tying (CDL Theorem G.10) + tie_weights consumer-facing API + SetCategoryDefaults opt-in marker for (Set, ×, 1)-flavoured ZSTs (v0.3.0). F-algebras / coalgebras with verify_commutes (CDL Defs 2.3, 2.8, B.2) + Z2 group-action GDL recovery test (CDL Example 2.6). Recursive FreeMnd<F, Z> / CofreeCmnd<F, Z> via GAT projection + ListEndo<A> / TreeEndo<A> bijections (CDL Prop B.18 / Examples B.19, B.20). Five architecture unrollers — FoldingRnn, RecursiveNn, UnfoldingRnn, MealyCell, MooreCell — with FreeMnd-equivalence tests reifying CDL Remark 2.13. Private hopf_fibration namespace stub for Dudzik's transcript-only carry-operation conjecture (NOT in published CDL paper; FE-paper-§6 evidence note confirms no preprint). No tokio, no serde, no rayon. |
These are separate repos that depend on catgraph and/or catgraph-physics:
| Repo | Purpose |
|---|---|
| catgraph-surreal | SurrealDB persistence layer for catgraph and catgraph-physics types (v0.11.1) |
| catgraph-coalition | Agent coalitions over SurrealDB live-query messaging; CatDL Quantale widening at v0.4.0 (private repo) |
| irreducible | Computational irreducibility framework (Gorard 2023) using catgraph and catgraph-physics (v0.6.5) |
Sibling repos pin to a single workspace umbrella tag (NOT each crate's individual version tag) for cargo source-identity deduplication. See CLAUDE.md for the full table.
| Umbrella tag | SHA | Crate versions |
|---|---|---|
v0.12.2 |
d0b30d5 |
catgraph v0.12.2 + catgraph-applied v0.5.4 + catgraph-magnitude v0.1.1 |
v0.13.0 |
4f8bda8 |
adds catgraph-dl v0.2.0 |
v0.13.1 |
ac699f6 |
catgraph-dl v0.3.0 |
v0.13.2 |
12ad5fd |
catgraph-dl v0.3.1 |
v0.13.3 |
541f943 |
catgraph-magnitude v0.3.0 + catgraph-applied v0.5.5 (current) |
cargo build --workspace
cargo test --workspace
cargo clippy --workspace -- -W clippy::pedanticEach crate has its own README and CLAUDE.md:
catgraph/README.md— strict F&S 2019 implementationcatgraph-physics/README.md— Wolfram-physics extensionscatgraph-applied/README.md— applied-CT extensionscatgraph-magnitude/README.md— BV 2025 magnitudecatgraph-dl/README.md— CDL ICML 2024 substrate
MIT — see LICENSE.