PQF Part III Local-Global Operators

This technical note shows how Higher Homotopy van Kampen Theory (HHvKT), atlas groupoids, and Yoneda’s lemma can be used directly inside the Possest–PQF framework to organize accessibility dynamics. The result is an operatorial, notation-clean pipeline: local thresholds Δ𝔽, endogenous cycles δ* (Recursio Intensitatis), and global indicators S_top, glued by HHvKT and read through Yoneda windows. Building on Brown–Glazebrook–Baianu’s categorical program, Part III supplies the local-to-global machinery that composes order-sensitive effects coherently across patches of the accessibility membrane. Key: Possest, PQF, Recursio Intensitatis (δ*), filtration operator (Δ𝔽), accessibility membrane, Yoneda window, atlas groupoid, double groupoids, Higher Homotopy van Kampen Theory (HHvKT), local–global composition, novelty detection, persistent homology, bottleneck distance, non-abelian invariants, topological data analysis (TDA), sheaf theory, applied category theory, Künneth transfer, operatorial ontology Related identifiers: – Cites: https://doi.org/10.5281/zenodo.17230263 (Part I) – Cites: https://doi.org/10.5281/zenodo.17230997 (Part II) – References: https://bangor.academia.edu/RonaldBrown (Brown’s page)