0NAZ Definition 4.8. A link homology for links in 33-spheres is a functor {link embeddings in oriented S≅S3link cobordisms in oriented Y≅S3×[0,1] up to isotopy rel ∂}→{bigraded abelian groupshomogeneous homomorphisms}\begin{Bmatrix}\textrm{link embeddings in oriented }S\cong S^{3}\\ \textrm{link cobordisms in oriented }Y\cong S^{3}\times{[0,1]}\textrm{ up to isotopy rel }\partial\end{Bmatrix}\xrightarrow{}\begin{Bmatrix}\textrm{bigraded abelian groups}\\ \textrm{homogeneous homomorphisms}\end{Bmatrix}