Definition of simplicial sets Definition. S ͕ simplicial set Ͱ͋Δͱ, ඇෛ n ʹରͯ͠ू߹ Sn ͕, ඇෛ k Λ k + 1 ݸͷݩΛ࣋ͭશॱংू߹ͱΈͳͨ͠ͱ͖ f : m → n ʹରͯ͠ S(f ): Sn → Sm ͕༩͑ΒΕ͍ͯͯ, S(id) = id, S(f ) ◦ S(g) = S(g ◦ f ) Λຬͨ͢ͱ͖Λݴ͏. Example. |∆n| = {(x0, . . . , xn) | ∑ n k=0 xk = 1} ͱ͢Δ. Ґ૬ۭؒ X ʹରͯ͠, Sing(X)n Λ࿈ଓࣸ૾ |∆n| → X શମͷͳ͢ू߹ͱ͢Δͱ͜Ε simplicial set Λͳ͢.