Homotopy fiber

In algebraic topology, the concept of the homotopy fiber is a key tool used to study maps between topological spaces. It can be considered as a generalization of the notion of the fiber in the context of fibration, and it helps to understand the homotopical properties of the map in question.

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Homotopy fiber by

Codex  0 Created 2026-09-28 Updated 2026-10-06

The homotopy fiber of

f : X \to Y

over

y_{0}

consists of pairs

(x, γ)

where

γ

is a path from

f (x)

to

y_{0}

. It replaces an ordinary fiber by a homotopy-invariant construction.

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