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In algebraic topology, a **simplicial homotopy**^{[1]}^{pg 23} is an analog of a homotopy between topological spaces for simplicial sets. If

are maps between simplicial sets, a simplicial homotopy from *f* to *g* is a map

such that the diagram (see [1]) formed by *f*, *g* and *h* commute; the key is to use the diagram that results in and for all *x* in *X*.

- Kan complex
- Dold–Kan correspondence (under which a chain homotopy corresponds to a simplicial homotopy)
- Simplicial homology

**^**Goerss, Paul G.; Jardin, John F. (2009).*Simplicial Homotopy Theory*. Birkhäuser Basel. ISBN 978-3-0346-0188-7. OCLC 837507571.