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.
npx skills add plurigrid/asi --skill categorical-compositiongit clone --depth 1 https://github.com/plurigrid/asiWrote 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.
[](https://agentmods.dev/skills/plurigrid/asi/categorical-composition)<a href="https://agentmods.dev/skills/plurigrid/asi/categorical-composition"><img src="https://agentmods.dev/badge/skills/plurigrid/asi/categorical-composition/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.
<a href="https://agentmods.dev/skills/plurigrid/asi/categorical-composition"><img src="https://agentmods.dev/badge/skills/plurigrid/asi/categorical-composition.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- NVIDIA SkillSpector pass
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.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00000 | $0.00667 |
| Opus 5 | $0.00000 | $0.00333 |
| Sonnet 5 | $0.00000 | $0.00133 |
| Haiku 4.5 | $0.00000 | $0.00067 |
Grade A, and why
categorical-composition 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 6d 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.
How it starts
The opening of the file, as written. The whole thing — 84 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Categorical Composition
Category: Phase 3 Core - Compositional Architecture Status: Skeleton Implementation Dependencies: None (foundational)
Overview
Implements categorical abstractions for compositional learning: Kan extensions for adapting between learning problems, higher adjunctions for bidirectional transformations, and functorial parameter transfer for compositional generalization.
Capabilities
- Kan Extensions: Left/right Kan extensions for problem adaptation
- Adjunctions: Adjoint functors for bidirectional transformations
- Functorial Transfer: Preserve structure across parameter spaces
- Compositional Architecture: Build complex systems from simple components
Core Components
-
Category Theory Primitives (
category_theory.jl)- Category, functor, natural transformation definitions
- Composition and identity laws
- Diagram chasing utilities
-
Kan Extensions (
kan_extensions.jl)- Left Kan extension (initial/colimit-based)
- Right Kan extension (terminal/limit-based)
- Pointwise computation formulas
-
Adjunctions (
adjunctions.jl)- Adjoint functor pairs
- Unit and counit natural transformations
- Triangle identities verification
-
Functorial Parameter Transfer (
functorial_transfer.jl)- Transfer neural network parameters via functors
- Preserve compositional structure
- Zero-shot generalization via categorical reasoning
Integration Points
- Input from: All Phase 3 skills (provides compositional framework)
- Output to: All Phase 3 skills (foundational abstraction)
- Coordinates with:
formal-verification-ai(correctness proofs)
Usage
using CategoricalComposition
# Define source and target categories
C = FiniteCategory(objects=[:A, :B], morphisms=Dict(:f => (:A, :B)))
D = FiniteCategory(objects=[:X, :Y, :Z], morphisms=Dict(:g => (:X, :Y), :h => (:Y, :Z)))
# Define functor F: C -> D
F = Functor(
source=C,
target=D,
object_map=Dict(:A => :X, :B => :Y),
morphism_map=Dict(:f => :g)
)
# Compute left Kan extension
G = Functor(source=C, target=Set, object_map=Dict(:A => [1,2], :B => [3,4]))
Lan_F_G = left_kan_extension(F, G)
# Verify adjunction
@assert check_adjunction(Lan_F_G, restriction_functor(F))
What ships with it
2 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
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.
- 6d ago First seen · 84 lines · 0 tokens per session scan A 1fd4b4d1fa87
categorical-composition is a skill published in the GitHub repository plurigrid/asi (62 stars, last pushed 2mo ago), licensed MIT. It costs nothing until one of its globs matches a file; then it loads 667 tokens. 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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