natural-transformations
Problem-solving strategies for natural transformations in category theory
Profile →npx skills add parcadei/Continuous-Claude-v3 --skill natural-transformations --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.
# Natural Transformations ## When to Use Use this skill when working on natural-transformations problems in category theory. ## Decision Tree 1. **Verify Naturality** - eta: F => G is natural transformation between functors F, G: C -> D - For each f: A -> B in C, diagram commutes: G(f) . eta_A = eta_B . F(f) - Write Lean 4: `theorem nat : η.app B ≫ G.map f = F.map f ≫ η.app A := η.naturality` 2. **Component Analysis** - eta_A: F(A) -> G(A) for each object A - Each component is morphism in target category D - Lean 4: `def η : F ⟶ G where app := fun X => ...` 3. **Natural Isomorphism** - Each component eta_A is isomorphism - Functors F and G are naturally isomorphic - Notation: F ≅ G (NatIso in Mathlib) 4. **Functor Category** - [C, D] has functors as objects - Natural transformations as morphisms - Vertical composition: Lean 4 `CategoryTheory.NatTrans.vcomp` - Horizontal composition: `CategoryTheory.NatTrans.hcomp` 5. **Yoneda Lemma Application** - Nat(Hom(A, -), F) ~ F(A) naturally in A - Lean 4: `CategoryTheory.yonedaEquiv` - Fully embeds C into [C^op, Set] - See: `.claude/skills/lean4-nat-trans/SKILL.md` for exact syntax ## Tool Commands ### Lean4_Naturality ```bash # Lean 4: the
- When to Use
- Decision Tree
- Tool Commands
- Lean4Naturality
- Lean4NatTrans
- Lean4Yoneda
- Lean4Build
- Cognitive Tools Reference
Lean 4: theorem nat : η.app B ≫ G.map f = F.map f ≫ η.app A := η.naturality Lean 4: def η : F ⟶ G where app := fun X => component_X Lean 4: CategoryTheory.yonedaEquiv -- Yoneda lemma lake build # Compiler-in-the-loop verification
What does the natural-transformations skill do?
Problem-solving strategies for natural transformations in category theory
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill natural-transformations --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 parcadei/Continuous-Claude-v3, a repository with 3,879 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.