### Solution manifolds for systems of differential equations.

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We raise the question of when a simplicial object in a catetgory is deemed contractible. The literature offers three definitions. One is the existence of an “extra degeneracy”, indexed by $-1$, which does not quite live up to the name. This can be strengthened to a “strong extra degeneracy". Another possibility is that it be homotopic to a constant simplicial object. Despite claims in the literature to the contrary, we show that all three are distinct concepts with strong extra degeneracy implies extra...

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