We describe how to formulate Khovanov’s functor-valued invariant of tangles in the language of bordered Heegaard Floer homology. We then give an alternate construction of Lawrence Roberts’ type and type structures in Khovanov homology, and his algebra , in terms of Khovanov’s theory of modules over the ring . We reprove invariance and pairing properties of Roberts’ bordered modules in this language. Along the way, we obtain an explicit generators-and-relations description of which may be of independent interest.
"On bordered theories for Khovanov homology." Algebr. Geom. Topol. 17 (3) 1557 - 1674, 2017. https://doi.org/10.2140/agt.2017.17.1557