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This PR includes (partial) proofs of the following:
StrictSegal
simplicial set are homotopic if and only if they are equal.OneTruncation
of aStrictSegal
simplicial set is a category.To avoid translating back and forth between paths (defined by directed paths of edges of type
X _[1]
) and homotopies, I have used the definition of homotopies from mathlib4#10006(comment). This differs slightly from the definition in #51. My tentative plan is to clean up the admitted proofs here, then open a new PR using the definition of homotopies from #51 for comparison.