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On the image of the almost strict Morse n-category under almost strict
n-functors

##
Sonja Hohloch

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.

Published 2014-04-12.

http://www.tac.mta.ca/tac/volumes/29/3/29-03.pdf

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