This paper is devoted to the study of algebraic structures leading to link
homology theories. The originally used structures of Frobenius algebra and/or
TQFT are modified in two directions. First, we refine 2-dimensional cobordisms
by taking into account their embedding into the three space. Secondly, we
extend the underlying cobordism category to a 2-category, where the usual
relations hold up to 2-isomorphisms. The corresponding abelian 2-functor is
called an extended quantum field theory (EQFT).