limits-colimits

limits-colimits is a skill for Claude Code from parcadei/Continuous-Claude-v3. It costs 14 tokens per session (533 once invoked), scanned A, original, MIT.

A guide to limits and colimits in category theory. Limits describe universal ways to combine objects, while colimits describe the corresponding ways to join them.

In plain words
What is it for?
Use it to identify limit or colimit types, verify universal properties, compute examples in sets, and reason about preservation in Lean 4.
Why use it?
It helps translate abstract universal properties into familiar constructions such as products, pullbacks, coproducts, and pushouts.

Skill for Claude Code

Written for Claude Code: allowed-tools in frontmatter. Also seen: reads .claude/ paths.

Good fit Use it to identify limit or colimit types, verify universal properties, compute examples in sets, and reason about preservation in Lean 4.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/parcadei/continuous-claude-v3/limits-colimits
About the project

Continuous-Claude-v3 is a Claude Code development environment that preserves working context between sessions, coordinates specialized agents, and stores project knowledge through ledgers, handoffs, and analysis tools. It is for people using Claude Code on ongoing or complex software work. Its catalogue entries are the skills, agents, hooks, plugin, and setting that provide its workflows and orchestration.

parcadei/Continuous-Claude-v3 · 3,938 stars · on GitHub

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

Any agent
npx skills add parcadei/Continuous-Claude-v3 --skill limits-colimits
Clone the repo
git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3

Made for: Claude Code.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for limits-colimits

README.md
[![agentmods](https://agentmods.dev/badge/skills/parcadei/continuous-claude-v3/limits-colimits/github.svg)](https://agentmods.dev/skills/parcadei/continuous-claude-v3/limits-colimits)
Your own site
<a href="https://agentmods.dev/skills/parcadei/continuous-claude-v3/limits-colimits"><img src="https://agentmods.dev/badge/skills/parcadei/continuous-claude-v3/limits-colimits/github.svg" alt="Measured on agentmods" height="20"></a>

Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

agentmods 80×15 button for limits-colimits

Your own site · 80×15
<a href="https://agentmods.dev/skills/parcadei/continuous-claude-v3/limits-colimits"><img src="https://agentmods.dev/badge/skills/parcadei/continuous-claude-v3/limits-colimits.svg" alt="Reviewed on agentmods" width="80" height="20"></a>
Per session 14 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 533 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe. Third-party audits
  • NVIDIA SkillSpector warn 7 Sept 2026
SkillSpector: 2 findings, up to medium

These are SkillSpector’s own severities. On a checked sample its high-severity flags on skills were ~96% false positives — a documented command, a public API, a “never do X” rule — so we show them as a caution to read, not a verdict. Why →

  • medium Agent Snooping · line 46
    Skill enumerates or reads other installed skills. Access to other skills' SKILL.md files or the skills directory reveals prompt instructions, capabilities, and secrets that should be invisible to peer skills.
    Fix: Remove all code or instructions that list or read other skills' files or directories. Skills should operate independently; cross-skill access is a privilege escalation.
  • medium Agent Snooping · line 73
    Skill enumerates or reads other installed skills. Access to other skills' SKILL.md files or the skills directory reveals prompt instructions, capabilities, and secrets that should be invisible to peer skills.
    Fix: Remove all code or instructions that list or read other skills' files or directories. Skills should operate independently; cross-skill access is a privilege escalation.
How audits are shown
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5.1 $0.00014 $0.00533
Opus 5 $0.00007 $0.00267
Sonnet 5 $0.00003 $0.00107
Haiku 4.5 $0.00001 $0.00053

Measured 9d ago against content hash 7c0298572cee, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-12, from the pricing page.

Security

Grade A, and why

limits-colimits scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 9d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

.claude/skills/math/category-theory/limits-colimits/SKILL.md · 74 lines

What it actually says

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

# 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.

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 9d ago First seen · 74 lines · 14 tokens per session scan A 7c0298572cee

Subscribe to this mod's changes

limits-colimits is a skill published in the GitHub repository parcadei/Continuous-Claude-v3 (3,938 stars, last pushed 7mo ago), licensed MIT. It adds 14 tokens to every session and 533 once invoked, about $0.0001 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-03.

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