ScalingStacks

Our computational advance is an explicit verification of this property for the 4-categories built from Khovanov–Rozansky link homology, specifically that link cobordisms represented by movies of the form

(1.1)

induce identity maps on the level of link homology. For a link homology theory, this property is equivalent to functoriality under link cobordisms in $S^{3}\times{[0,1]}$, which has important consequences beyond the scope of this paper, such as the injectivity of maps induced by ribbon concordances, see Kang [Kan19].