Example Sentences

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For example, in π ∞ X the objects and arrows are the points and the paths—no longer considered up to wiggling—while the higher-dimensional transformations encode the higher homotopies.

From Scientific American • Sep. 14, 2021

These deformations, which are technically called homotopies, are necessary for the composition of paths to define an associative operation, as is required by a category.

From Scientific American • Sep. 14, 2021

But contractability guarantees that any two composite paths are homotopic, any two homotopies relating two composite paths are connected by a higher homotopy, and so on.

From Scientific American • Sep. 14, 2021