In an earlier work, we constructed the almost strict Morse n-category $\mathcal X$ which extends Cohen and Jones and 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 $\mathcal G : \mathcal X \to \mathcal W$.
Keywords: n-category, Morse theory, functors, moduli spaces
2010 MSC: 18B99, 18D99, 55U99, 58E05
Theory and Applications of Categories, Vol. 29, 2014, No. 3, pp 21-47.