  We introduce a Heegaard-Floer homology functor from the category of oriented
links in closed $3$-manifolds and oriented surface cobordisms in $4$-manifolds
connecting them to the category of $\mathbb{F}[v]$-modules and
$\mathbb{F}[v]$-homomorphisms between them, where $\mathbb{F}$ is the field
with two elements. In comparison with previously defined TQFTs for decorated
links and link cobordisms, the construction of this paper has the advantage of
being independent from the decoration. Some of the basic properties of this
functor are also explored.
