in the following sense: if 1=''f''₁, ''g''₁ : ''X'' -> ''Y'' are homotopic, and 1=''f''₂, ''g''₂ : ''Y'' -> ''Z'' are homotopic, then their compositions 1=''f''₂ ? ''f''₁ and 1=''g''₂ ? ''g''₁ : ''X'' -> ''Z'' are also homotopic.

Examples

* If are given by and , then the map given by is a homotopy between them.
* More generally, if is a convex subset of Euclidean space

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