limits-colimits
Problem-solving strategies for limits colimits in category theory
Profile →npx skills add parcadei/Continuous-Claude-v3 --skill limits-colimits --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.
# Limits Colimits ## When to Use Use this skill when working on limits-colimits problems in category theory. ## Decision Tree 1. **Identify Limit Type** - Product: limit of discrete diagram - Equalizer: limit of parallel pair f, g: A -> B - Pullback: limit of A -> C <- B - Terminal object: limit of empty diagram - Lean 4: `CategoryTheory.Limits` namespace 2. **Verify Universal Property** - Cone from L with projections pi_i: L -> D_i - For any cone from X, unique morphism u: X -> L - Triangles commute: pi_i . u = cone_i - Lean 4: `IsLimit.lift` gives the unique morphism 3. **Colimit (Dual)** - Coproduct: colimit of discrete diagram - Coequalizer: colimit of parallel pair - Pushout: colimit of A <- C -> B - Initial object: colimit of empty diagram 4. **Compute Limits Concretely** - In Set: product = Cartesian product - Equalizer = {x | f(x) = g(x)} - Pullback = {(a,b) | f(a) = g(b)} - `sympy_compute.py solve "f(a) == g(b)"` 5. **Preservation** - Right adjoint preserves limits - Left adjoint preserves colimits - Representable functors preserve limits - Lean 4: `Adjunction.rightAdjointPreservesLimits` - See: `.claude/skills/lean4-limits/SKILL.md` for exact syntax ## Tool Commands ### L
- When to Use
- Decision Tree
- Tool Commands
- Lean4Limit
- Lean4Universal
- SympyPullback
- Lean4Build
- Cognitive Tools Reference
Lean 4: import CategoryTheory.Limits.Shapes.Products Lean 4: IsLimit.lift cone -- unique morphism from universal property uv run python -m runtime.harness scripts/sympy_compute.py solve "f(a) == g(b)" lake build # Compiler-in-the-loop verification
What does the limits-colimits skill do?
Problem-solving strategies for limits colimits in category theory
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill limits-colimits --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.