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Agent skill

Natural Transformations

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for natural transformations in category theory

MITAuto-check: notes

Install Natural Transformations

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill natural-transformations -a claude-code

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

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 natural-transformations --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/natural-transformations .claude/skills/natural-transformations && 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
natural-transformations
GitHub stars
3.9k
Used in
1 other repo
Token cost
~461 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 natural transformations in category theory

  • Works in 5 steps: Verify Naturality → Component Analysis → Natural Isomorphism → …
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Cognitive Tools Reference
  • Instructions only: no scripts, shell commands, URLs or credentials in SKILL.md

What it does

Natural Transformations is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for natural transformations in category theory

Its SKILL.md is about 460 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

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.

Example prompts

  • “/natural-transformations”

Requirements

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

Workflow steps

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

  1. Verify Naturality
  2. Component Analysis
  3. Natural Isomorphism
  4. Functor Category
  5. Yoneda Lemma Application

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

    No scripts in the folder and no shell commands in SKILL.md (its code samples are bash).

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

  • Network

    No URLs in SKILL.md.

    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

Natural Transformations loads about 461 tokens when it runs. Until then it costs about 24 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
~24
When it runs · the whole SKILL.md, loaded when a task matches
~461

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, ~461 tokens.

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

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: theorem nat : η.app B ≫ G.map f = F.map f ≫ η.app A := η.naturality
Lean4_Nat_Trans
bash
# Lean 4: def η : F ⟶ G where app := fun X => component_X
Lean4_Yoneda
bash
# Lean 4: CategoryTheory.yonedaEquiv -- Yoneda lemma
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/natural-transformations 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

Natural Transformations 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.

Natural Transformations compared with similar skills
SkillStarsUsed inTokensAuto-checkLicenceRepo updated
Natural Transformations this skillparcadei/Continuous-Claude-v33.9k1 repos~461Automated safety check: NotesMIT
TransformersK-Dense-AI/scientific-agent-skills48k1 repos~2.8kAutomated safety check: NotesApache-2.0
Good Strategy Bad Strategywondelai/skills2.4k—~4.8kAutomated safety check: PassMIT
Product Strategyphuryn/pm-skills27k—~1.2kAutomated safety check: PassMIT
Vc Problem Solvingwithkynam/vibecode-pro-max-kit1.1k1 repos~1.1kAutomated safety check: PassMIT
Launch Strategyalirezarezvani/claude-skills28k—~1.4kAutomated safety check: PassMIT

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Questions about Natural Transformations

What does Natural Transformations do?

Problem-solving strategies for natural transformations in category theory. Natural Transformations is an agent skill from parcadei/Continuous-Claude-v3.

How do I install Natural Transformations in Claude Code?

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

How do I install Natural Transformations in Codex?

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

Can I use Natural Transformations 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 natural-transformations -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/natural-transformations, .gemini/skills/natural-transformations, .github/skills/natural-transformations and .opencode/skills/natural-transformations in your project.

What does Natural Transformations need to run?

SKILL.md names no scripts, command-line tools or credentials: Natural Transformations is instructions for the agent only. Its frontmatter pre-approves these tools: Bash, Read.

Does Natural Transformations access the network?

SKILL.md contains no URLs. Any network use would come from the scripts or tools the agent runs. This is read from the text; nothing was executed.

Is Natural Transformations 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 Natural Transformations use?

Natural Transformations 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 Natural Transformations use?

About 461 tokens (SKILL.md is roughly 1.8k 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 Natural Transformations?

Skills that share tags, products or a category with Natural Transformations: Transformers (K-Dense-AI/scientific-agent-skills, 48k stars), Good Strategy Bad Strategy (wondelai/skills, 2.4k stars), Product Strategy (phuryn/pm-skills, 27k stars) and Vc Problem Solving (withkynam/vibecode-pro-max-kit, 1.1k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Natural Transformations?

parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,943 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.