Title: Strong Khovanov-Floer Theories and Functoriality,
Abstract: We provide a unified framework for proving Reidemeister-invariance and
functoriality for a wide range of link homology theories. These include Lee
homology, Heegaard Floer homology of branched double covers, singular instanton
homology, and \Szabo's geometric link homology theory. We follow Baldwin,
Hedden, and Lobb (arXiv:1509.04691) in leveraging the relationships between
these theories and Khovanov homology. We obtain stronger functoriality results
by avoiding spectral sequences and instead showing that each theory factors
through Bar-Natan's cobordism-theoretic link homology theory.