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Simplicial homotopy : ウィキペディア英語版
Simplicial homotopy

In algebraic topology, a simplicial homotopy is an analog of a homotopy between topological spaces for simplicial sets. If
:f, g: X \to Y
are maps between simplicial sets, a simplicial homotopy from ''f'' to ''g'' is a map
:h: X \times \triangle^ \to Y
such that the obvious diagram (see ()) formed by ''f'', ''g'' and ''h'' commute; the key is to use the diagram that results in f(x) = h(x, 0) and g(x) = h(x, 1) for all ''x'' in ''X''.
== See also ==

*Dold–Kan correspondence (under which a chain homotopy corresponds to a simplicial homotopy)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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