oapply-colimit

oapply: Operad algebra evaluation via colimits. Composes machines/resource sharers.

16 stars

byplurigrid

View on GitHub Installation ↓

Best use case

oapply-colimit is best used when you need a repeatable AI agent workflow instead of a one-off prompt.

oapply: Operad algebra evaluation via colimits. Composes machines/resource sharers.

Teams using oapply-colimit should expect a more consistent output, faster repeated execution, less prompt rewriting.

When to use this skill

You want a reusable workflow that can be run more than once with consistent structure.

When not to use this skill

You only need a quick one-off answer and do not need a reusable workflow.
You cannot install or maintain the underlying files, dependencies, or repository context.

Installation

Claude Code / Cursor / Codex

$curl -o ~/.claude/skills/oapply-colimit/SKILL.md --create-dirs "https://raw.githubusercontent.com/plurigrid/asi/main/ies/music-topos/.agents/skills/oapply-colimit/SKILL.md"

Manual Installation

Download SKILL.md from GitHub
Place it in .claude/skills/oapply-colimit/SKILL.md inside your project
Restart your AI agent — it will auto-discover the skill

How oapply-colimit Compares

Feature / Agent	oapply-colimit	Standard Approach
Platform Support	Not specified	Limited / Varies
Context Awareness	High	Baseline
Installation Complexity	Unknown	N/A

Frequently Asked Questions

What does this skill do?

oapply: Operad algebra evaluation via colimits. Composes machines/resource sharers.

Where can I find the source code?

You can find the source code on GitHub using the link provided at the top of the page.

SKILL.md Source

# oapply-colimit Skill

## Core Pattern

`oapply` computes **colimit** of component diagram over wiring pattern:

```julia
using AlgebraicDynamics

# Pattern + components → composite
composite = oapply(wiring_diagram, [machine1, machine2, ...])
```

## Two Composition Modes

| Mode | Type | Gluing | Example |
|------|------|--------|---------|
| **Undirected** | ResourceSharer | Pushout (shared state) | Lotka-Volterra |
| **Directed** | Machine | Wiring (signal flow) | Control systems |

## Implementation

```julia
function oapply(d::UndirectedWiringDiagram, xs::Vector{ResourceSharer})
    # 1. Coproduct of state spaces
    S = coproduct((FinSet ∘ nstates).(xs))
    
    # 2. Pushout identifies shared variables
    S′ = pushout(portmap, junctions)
    
    # 3. Induced dynamics sum at junctions
    return ResourceSharer(induced_interface, induced_dynamics)
end
```

## GF(3) Triads

```
schema-validation (-1) ⊗ acsets (0) ⊗ oapply-colimit (+1) = 0 ✓
interval-presheaf (-1) ⊗ algebraic-dynamics (0) ⊗ oapply-colimit (+1) = 0 ✓
```

## References

- Libkind "An Algebra of Resource Sharers" arXiv:2007.14442
- AlgebraicJulia/AlgebraicDynamics.jl

Related Skills

We are still matching the closest adjacent skills for this page. In the meantime, continue through the full directory.