oapply-colimit Skill
oapply-colimit
oapply: Operad algebra evaluation via colimits. Composes machines/resource sharers.
SKILL.md
Full skill instructions
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