In an earlier work, we constructed the almost strict Morse n-category X which extends Cohen Sz Jones Sz Segal's flow category. In this article, we define two other almost strict n-categories V and W where V is based on homomorphisms between real vector spaces and 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 F: X -> V and G: X -> W