"Grothendieck conjectured that the infinity groupoid captures all information about a topological space up to weak homotopy equivalence" The homotopy hypothesi

"Grothendieck conjectured that the infinity groupoid captures all information about a topological space up to weak homotopy equivalence" The homotopy hypothesis has something mystical about it. https://math.ucr.edu/home/baez/homotopy/homotopy.pdf https://math.ucr.edu/home/baez/homotopy/homotopy.pdf