infinity-operads
∞-Operads for pairwise/tritwise Cat# interactions with lazy ACSet materialization unifying effective, realizability, and Grothendieck topoi via dendroidal Segal spaces.
npx skills add majiayu000/claude-skill-registry --skill infinity-operads-plurigrid-asi-2 --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# ∞-Operads Skill (ERGODIC 0) > *"The dendroidal nerve carries operads to ∞-operads exactly as the simplicial nerve carries categories to ∞-categories."* > — Cisinski-Moerdijk **Trit**: 0 (ERGODIC) **Color**: #26D826 (Green) **Role**: Coordinator/Transporter **XIP**: Dendroidal (Ω-set) → Cat# horizontal morphism ## Core Insight: Pairwise = Bicomodule, Tritwise = Equipment Tensor | Interaction Type | Cat# Structure | Operad View | Lazy ACSet | |------------------|----------------|-------------|------------| | **Pairwise** | Bicomodule composition in Prof | Binary operation | `JOIN` on demand | | **Tritwise** | Equipment tensor ⊗ (GF(3) balanced) | Ternary tree grafting | Materialized view | | **N-ary** | ∞-operad algebra evaluation | Dendroidal composition | Recursive CTE | ## 1. Dendroidal Sets and ∞-Operads ### Ω-Category (Tree Category) Objects: **Finite rooted trees** T with labelled edges Morphisms: **Face/degeneracy maps** (like Δ for simplicial sets) ``` r /|\ e1 e2 e3 ∈ Ω (corolla with 3 inputs) ``` ### Dendroidal Set Functor `X: Ω^op → Set` - `X(T)` = set of T-shaped operations - Face maps = composition - Degeneracy maps = identity insertion ### ∞-Operad as Dendroidal Segal
- Core Insight: Pairwise = Bicomodule, Tritwise = Equipment Tensor
- 1. Dendroidal Sets and ∞-Operads
- Ω-Category (Tree Category)
- Dendroidal Set
- ∞-Operad as Dendroidal Segal Space
- 2. Cat# Equipment ↔ ∞-Operads
- Horizontal Morphisms as Pairwise Interactions
- Equipment Tensor as Tritwise Interactions
- ∞-Operad Algebra = N-ary Interaction
- 3. Lazy ACSet Materialization
- Schema: Lazy Geometric Morphisms
- Lazy Evaluation via Category of Elements
- DuckDB Lazy Views
- 4. Topos Unification: Effective ≅ Realizability ≅ Grothendieck
Query pairwise bicomodule interactions just infinity-pairwise source=kan-extensions target=operad-compose Find all GF(3) balanced tritwise interactions just infinity-tritwise --balanced Lazy materialize geometric morphisms for a skill just infinity-geom-morph --skill=acsets Show topos unification status just infinity-topos-unify Generate ∞-operad algebra evaluation diagram just infinity-algebra-eval --operad=E_n --arity=3
What does the infinity-operads skill do?
∞-Operads for pairwise/tritwise Cat# interactions with lazy ACSet materialization unifying effective, realizability, and Grothendieck topoi via dendroidal Segal spaces.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill infinity-operads-plurigrid-asi-2 --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.