limits-colimits skill

by parcadei·parcadei/Continuous-Claude-v3·3.9k stars·MIT

Problem-solving strategies for limits colimits in category theory

A100/100content scan

Is the limits-colimits skill safe?

Clean: nothing in its files matched our rules. We read 1 file in the folder on 2026-09-28.

No findings.

Install the limits-colimits skill

A skill is a folder. Copy it into your agent's skills folder and the agent loads it when the task matches its description.

git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git /tmp/Continuous-Claude-v3
mkdir -p ~/.claude/skills
cp -r /tmp/Continuous-Claude-v3/.claude/skills/math/category-theory/limits-colimits ~/.claude/skills/limits-colimits

available in every project

In the Claude apps, zip the folder and upload it from the Skills settings. The folder on GitHub

The instructions your agent would load

SKILL.md as published, without the frontmatter. Read it on GitHub

Limits Colimits

When to Use

Use this skill when working on limits-colimits problems in category theory.

Decision Tree

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

Verify Universal Property

Cone from L with projections pii: L -> Di
For any cone from X, unique morphism u: X -> L
Triangles commute: pii . u = conei
Lean 4: IsLimit.lift gives the unique morphism

Colimit (Dual)

Coproduct: colimit of discrete diagram
Coequalizer: colimit of parallel pair
Pushout: colimit of A <- C -> B
Initial object: colimit of empty diagram

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)"

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

Lean4_Limit

# Lean 4: import CategoryTheory.Limits.Shapes.Products

Lean4_Universal

# Lean 4: IsLimit.lift cone -- unique morphism from universal property

Sympy_Pullback

uv run python -m runtime.harness scripts/sympy_compute.py solve "f(a) == g(b)"

Lean4_Build

lake build  # Compiler-in-the-loop verification

Cognitive Tools Reference

See .claude/skills/math-mode/SKILL.md for full tool documentation.

More skills from parcadei/Continuous-Claude-v3

Aagent-context-isolationAgent Context Isolation
Aagent-orchestrationAgent Orchestration Rules
Aagentic-workflowAgentic Workflow Pattern
Aagentica-claude-proxyGuide for integrating Agentica SDK with Claude Code CLI proxy
Aagentica-infrastructureReference guide for Agentica multi-agent infrastructure APIs
Aagentica-promptsWrite reliable prompts for Agentica/REPL agents that avoid LLM instruction ambiguity
Aagentica-sdkBuild Python agents with Agentica SDK - @agentic decorator, spawn(), persistence, MCP integration
Aagentica-serverAgentica server + Claude proxy setup - architecture, startup sequence, debugging
Aagentica-spawnSpawn Agentica multi-agent patterns
Aanalytic-functionsProblem-solving strategies for analytic functions in complex analysis
Aast-grep-findAST-based code search and refactoring via ast-grep MCP
Aasync-repl-protocolAsync REPL Protocol

All agent skills → · MCP servers