Title: On the image of the almost strict Morse n-category under almost strict n-functors,
Abstract: In an earlier work, we constructed the almost strict Morse $n$-category
$\mathcal X$ which extends Cohen $\&$ Jones $\&$ Segal's flow category. In this
article, we define two other almost strict $n$-categories $\mathcal V$ and
$\mathcal W$ where $\mathcal V$ is based on homomorphisms between real vector
spaces and $\mathcal W$ consists of tuples of positive integers. The Morse
index and the dimension of the Morse moduli spaces give rise to almost strict
$n$-category functors $\mathcal F : \mathcal X \to \mathcal V$ and $\mathcal G
: \mathcal X \to \mathcal W$.