Short, math‑heavy write‑up (PDF, 11 pp.) that re‑derives the classical initial‑algebra construction for ω‑continuous endofunctors and then isolates a “Node Deletion Theorem”: remove a single object from the building chain and the theorem tells you exactly which arrows vanish in the resulting colimit. In practical terms it gives a provably‑safe recipe for cutting nodes out of abstract‑syntax trees, graphs or other inductive data without reconstructing the whole structure—think incremental compilers, program transformers, or graph‑rewrite engines. The note also sketches a joint‑fixed‑point extension (Bekić‑style) and invites feedback, counter‑examples and real‑world applications. Comments and pointers to prior art welcome!
Short, math‑heavy write‑up (PDF, 11 pp.) that re‑derives the classical initial‑algebra construction for ω‑continuous endofunctors and then isolates a “Node Deletion Theorem”: remove a single object from the building chain and the theorem tells you exactly which arrows vanish in the resulting colimit. In practical terms it gives a provably‑safe recipe for cutting nodes out of abstract‑syntax trees, graphs or other inductive data without reconstructing the whole structure—think incremental compilers, program transformers, or graph‑rewrite engines. The note also sketches a joint‑fixed‑point extension (Bekić‑style) and invites feedback, counter‑examples and real‑world applications. Comments and pointers to prior art welcome!