plurigrid/oapply-colimit
ies/music-topos/.agents/skills/oapply-colimit/SKILL.md
oapply: Operad algebra evaluation via colimits. Composes machines/resource sharers.
$ install --global
skillsauthnpx skillsauth add plurigrid/asi oapply-colimitInstall this skill globally with one command. Works with Claude Code, Cursor, and Windsurf.
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Last scanned: Apr 24, 2026, 8:43 PM1.9s1 file scanned
SKILL.md
- name:
- oapply-colimit
- description:
- oapply: Operad algebra evaluation via colimits. Composes machines/resource sharers.
- source:
- AlgebraicJulia/AlgebraicDynamics.jl
- license:
- MIT
- trit:
- +1
oapply-colimit Skill
Core Pattern
oapply computes colimit of component diagram over wiring pattern:
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
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
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