A type D structure in Khovanov homology

We describe the first part of a gluing theory for the bigraded Khovanov homology with ZZ-coefficients. This part associates a type D structure to a tangle properly embedded in a half-space and proves that the homotopy class of the type D structure is an invariant of the isotopy class of the tangle. The construction is modeled off bordered Heegaard–Floer homology, but uses only combinatorial/diagrammatic methods.