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