Combinatorial Descriptions of Homotopy Groups
نویسنده
چکیده
Let X be a cofunctor from O to sets. Let Xn = X({0, 1, · · · , n}). The face function dj : Xn → Xn−1 is induced by the inclusion d : {0, · · · , n − 1} → {0, · · ·n} with d(i) = i for i < j, d(i) = i + 1 for i ≥ j for 0 ≤ j ≤ n. The degeneracy function sj : Xn → Xn+1 is induced by s : {0, · · · , n+ 1} → {0, · · · , n} with s(i) = i for i ≤ j and s(i) = i− 1 for i > j for 0 ≤ j ≤ n. The simplicial identities holds for di’s and sj’s. Conversely, any simplicial set defines uniquely a cofunctor from O to sets.
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تاریخ انتشار 2000