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Agent skill

Limits Colimits

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for limits colimits in category theory

MITAuto-check: notesResearch & Science

Install Limits Colimits

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill limits-colimits -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 limits-colimits --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.claude/skills/math/category-theory/limits-colimits .claude/skills/limits-colimits && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
limits-colimits
GitHub stars
3.9k
Used in
1 other repo
Token cost
~472 tokens
SKILL.md length
169 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for limits colimits in category theory

  • Works in 5 steps: Identify Limit Type → Verify Universal Property → Colimit (Dual) → …
  • Research & Science work in your project
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Cognitive Tools Reference
  • Calls uv

What it does

Limits Colimits is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for limits colimits in category theory

Its SKILL.md is about 470 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

It sits in Research & Science. The repository describes itself as: Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows. The licence is MIT.

When your agent uses it

  • Research & Science work in your project

Example prompts

  • “/limits-colimits”

Requirements

  • Python 3
  • Pre-approved tools (allowed-tools): Bash, Read

Workflow steps

5 steps, taken from the first numbered list in SKILL.md.

  1. Identify Limit Type
  2. Verify Universal Property
  3. Colimit (Dual)
  4. Compute Limits Concretely
  5. Preservation

What it can do on your machine

Read from SKILL.md and the folder at commit d07ff4b. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves these tools, so the agent can use them without asking each time:

    • Bash
    • Read

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    Shell commands in SKILL.md call:

    • uv

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md. Its commands use uv, which can reach the network depending on how they are called.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Limits Colimits loads about 472 tokens when it runs. Until then it costs about 20 tokens; SKILL.md has 169 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~20
When it runs · the whole SKILL.md, loaded when a task matches
~472

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check: notes

The automated check noted patterns worth knowing about, such as sudo or a known installer.

  • NotePre-approves every shell command (allowed-tools: Bash)SKILL.md
    allowed-tools: Bash, Read

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from parcadei/Continuous-Claude-v3 at commit d07ff4b, republished under its MIT licence (© parcadei). 169 words, ~472 tokens.

Download SKILL.mdSave it as .claude/skills/limits-colimits/SKILL.md (or your agent's skills folder).
name
limits-colimits
description
Problem-solving strategies for limits colimits in category theory
allowed-tools
Bash, Read

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

Lean4_Limit
bash
# Lean 4: import CategoryTheory.Limits.Shapes.Products
Lean4_Universal
bash
# Lean 4: IsLimit.lift cone -- unique morphism from universal property
Sympy_Pullback
bash
uv run python -m runtime.harness scripts/sympy_compute.py solve "f(a) == g(b)"
Lean4_Build
bash
lake build  # Compiler-in-the-loop verification

Cognitive Tools Reference

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

© parcadei, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

Just SKILL.md in .claude/skills/math/category-theory/limits-colimits of parcadei/Continuous-Claude-v3.

Open the folder on GitHubat commit d07ff4b

Used in 1 other repository

We found 1 copy of this SKILL.md (exact, near-identical or edited) in other folders, from 1 other GitHub owner. This page covers the copy in parcadei/Continuous-Claude-v3, which our catalogue first saw on October 7, 2026.

Compare with similar skills

Limits Colimits next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

Limits Colimits compared with similar skills
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Limits Colimits this skillparcadei/Continuous-Claude-v33.9k1 repos~472Automated safety check: NotesMIT
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GitHub Deep Researchbytedance/deer-flow83k5 repos~1.3kAutomated safety check: PassMIT
Nature Paper CardYuan1z0825/nature-skills46k2 repos~2.1kAutomated safety check: PassApache-2.0
Read arXiv Paperkarpathy/nanochat58k2 repos~494Automated safety check: PassMIT
Content Research Writerweapp-tailwindcss/weapp-tailwindcss1.9k25 repos~3.5kAutomated safety check: PassMIT

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Categories

Questions about Limits Colimits

What does Limits Colimits do?

Problem-solving strategies for limits colimits in category theory. Limits Colimits is an agent skill from parcadei/Continuous-Claude-v3.

When should I use Limits Colimits?

Limits Colimits fits situations like: research & Science work in your project.

How do I install Limits Colimits in Claude Code?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill limits-colimits -a claude-code`. Or copy the skill folder (.claude/skills/math/category-theory/limits-colimits in parcadei/Continuous-Claude-v3) into .claude/skills/limits-colimits in your project. Claude Code loads it when a task matches its description.

How do I install Limits Colimits in Codex?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill limits-colimits -a codex`. Or copy the skill folder (.claude/skills/math/category-theory/limits-colimits in parcadei/Continuous-Claude-v3) into .agents/skills/limits-colimits in your project. Codex loads it when a task matches its description.

Can I use Limits Colimits in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add parcadei/Continuous-Claude-v3 --skill limits-colimits -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/limits-colimits, .gemini/skills/limits-colimits, .github/skills/limits-colimits and .opencode/skills/limits-colimits in your project.

What does Limits Colimits need to run?

Going by SKILL.md and its folder, Limits Colimits needs the command-line tools its instructions call (uv). Our summary lists: Python 3. Its frontmatter pre-approves these tools: Bash, Read.

Does Limits Colimits access the network?

SKILL.md contains no URLs. Its commands use uv, which can reach the network depending on how they are called. This is read from the text; nothing was executed.

Is Limits Colimits safe to install?

Our automated static check of SKILL.md found notes only (pre-approves every shell command (allowed-tools: bash)), nothing it rates as a warning. It is not a guarantee. Review the folder before installing.

What licence does Limits Colimits use?

Limits Colimits is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Limits Colimits use?

About 472 tokens (SKILL.md is roughly 1.9k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.

What are the alternatives to Limits Colimits?

Skills that share tags, products or a category with Limits Colimits: Hypothesis Generation (spacering-net/codeg, 3.8k stars), GitHub Deep Research (bytedance/deer-flow, 83k stars), Nature Paper Card (Yuan1z0825/nature-skills, 46k stars) and Read arXiv Paper (karpathy/nanochat, 58k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Limits Colimits?

parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,940 GitHub stars. The repository holds 141 skills in this directory. The repository was last updated on January 26, 2026.

Source: parcadei/Continuous-Claude-v3 on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.