# Associahedral categories, particles and Morse functor

@article{Welschinger2009AssociahedralCP, title={Associahedral categories, particles and Morse functor}, author={Jean-Yves Welschinger}, journal={arXiv: Symplectic Geometry}, year={2009} }

Every smooth manifold contains particles which propagate. These form objects and morphisms of a category equipped with a functor to the category of Abelian groups, turning this into a 0 + 1 topological eld theory. We investigate the algebraic structure of this category, intimately related to the structure of Stashe’s polytops, introducing the notion of associahedral categories. An associahedral category is preadditive and close to being strict monoidal. Finally, we interpret Morse-Witten theory…

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