  We generalize our previous work on categorification of Kauffman bracket skein
module of surfaces, by extending our homology to tangles in cylinders over
surfaces, F x [0,1]. Our homology of 0-tangles and 1-tangles in D^3 coincides
(up to normalization) with Khovanov link homology and the reduced Khovanov link
homology.
  We prove the basic properties of our homology. In particular, the short exact
sequence of homologies of skein related tangles and the Kunneth formula for the
tensor product of tangles.
