I'll begin by discussing the construction of the Khovanov
homology groups from a link. I'll then discuss a framework that allows
the construction of similar objects in many contexts, in particular
recovering Lipshitz and Sarkar's refinement to an object in stable
homotopy whose homology groups recover Khovanov homology.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/TopologySeminar