We further study the symplectic Khovanov homology of Seidel and Smith and its
generalization to even tangles. This homology theory is a conjectural geometric
model for Khovanov homology. In this paper we uncover structures on symplectic
Khovanov homology which have analogues in Khovanov homology. To each elementary
(as well as minimal) cobordism between two tangles we associate a homomorphism
between the symplectic Khovanov homology groups of the two tangles.
We define the symplectic analogues $H_{s}^m$ of Khovanov's arc algebras and
equip the symplectic Khovanov homology of an $(m,n)$-tangle with the structure
of an $(H_{s}^m,H_{s}^n)$-bimodule. We show that $H_{s}^m$ and Khovanov's $H^m$
are isomorphic as associative algebras over $\Z/2$. We also obtain a skein
exact triangle for symplectic Khovanov homology which resembles the one for
Khovanov homology.