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Agent skill

Categories Functors

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for categories functors in category theory

MITAuto-check: notes

Install Categories Functors

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill categories-functors -a claude-code

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

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 categories-functors --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/categories-functors .claude/skills/categories-functors && 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
categories-functors
GitHub stars
3.9k
Used in
1 other repo
Token cost
~468 tokens
SKILL.md length
178 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for categories functors in category theory

  • Works in 5 steps: Verify Category Axioms → Check Functor Properties → Functor Types → …
  • 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

Categories Functors is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for categories functors 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.

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

  • “/categories-functors”

Requirements

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

Workflow steps

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

  1. Verify Category Axioms
  2. Check Functor Properties
  3. Functor Types
  4. Common Functors
  5. Verify with Lean 4

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

Categories Functors loads about 468 tokens when it runs. Until then it costs about 22 tokens; SKILL.md has 178 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~22
When it runs · the whole SKILL.md, loaded when a task matches
~468

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). 178 words, ~468 tokens.

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

Categories Functors

When to Use

Use this skill when working on categories-functors problems in category theory.

Decision Tree

  1. Verify Category Axioms

    • Objects and morphisms (arrows) defined?
    • Identity morphism for each object: id_A: A -> A
    • Composition associative: (f . g) . h = f . (g . h)
    • Write Lean 4: theorem assoc : (f ≫ g) ≫ h = f ≫ (g ≫ h) := Category.assoc

  2. Check Functor Properties

    • F: C -> D maps objects to objects, arrows to arrows
    • Preserves identity: F(id_A) = id_{F(A)}
    • Preserves composition: F(g . f) = F(g) . F(f)
    • Write Lean 4: theorem comp : F.map (g ≫ f) = F.map g ≫ F.map f := F.map_comp

  3. Functor Types

    • Covariant: preserves arrow direction
    • Contravariant: reverses arrow direction
    • Faithful/Full: injective/surjective on Hom-sets
    • Equivalence: full, faithful, essentially surjective

  4. Common Functors

    • Forgetful functor: forgets structure (e.g., Grp -> Set)
    • Free functor: left adjoint to forgetful
    • Hom functor: Hom(A, -) or Hom(-, B)
    • Power set functor: Set -> Set via X |-> P(X)

  5. Verify with Lean 4

    • Compiler-in-the-loop: write proof, lake build checks
    • Mathlib has full category theory library
    • See: .claude/skills/lean4-functors/SKILL.md for exact syntax

Tool Commands

Lean4_Category
bash
# Lean 4 with Mathlib: import CategoryTheory.Category.Basic
Lean4_Functor
bash
# Lean 4: theorem map_comp (F : C ⥤ D) : F.map (g ≫ f) = F.map g ≫ F.map f := F.map_comp
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/categories-functors 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

Categories Functors 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.

Categories Functors compared with similar skills
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Categories Functors this skillparcadei/Continuous-Claude-v33.9k1 repos~468Automated safety check: NotesMIT
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Vc Problem Solvingwithkynam/vibecode-pro-max-kit1.1k2 repos~1.1kAutomated safety check: PassMIT
Launch Strategyalirezarezvani/claude-skills28k—~1.4kAutomated safety check: PassMIT
Pricing Strategyalirezarezvani/claude-skills28k1 repos~3.5kAutomated safety check: PassMIT

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Questions about Categories Functors

What does Categories Functors do?

Problem-solving strategies for categories functors in category theory. Categories Functors is an agent skill from parcadei/Continuous-Claude-v3.

How do I install Categories Functors in Claude Code?

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

How do I install Categories Functors in Codex?

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

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

What does Categories Functors need to run?

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

Does Categories Functors 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 Categories Functors 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 Categories Functors use?

Categories Functors 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 Categories Functors use?

About 468 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 Categories Functors?

Skills that share tags, products or a category with Categories Functors: Good Strategy Bad Strategy (wondelai/skills, 2.4k stars), Product Strategy (phuryn/pm-skills, 27k stars), Vc Problem Solving (withkynam/vibecode-pro-max-kit, 1.1k stars) and Launch Strategy (alirezarezvani/claude-skills, 28k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Categories Functors?

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.