Morse complexes of compact Lie monoids are equipped with f-bialgebra structures that define infinity-functors, extending to closed manifolds and manifolds with compact Lie group actions.
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The Morse complex is an $\infty$-functor
Morse complexes of compact Lie monoids are equipped with f-bialgebra structures that define infinity-functors, extending to closed manifolds and manifolds with compact Lie group actions.