Simplicial homotopy
From HandWiki
In algebraic topology, a simplicial homotopy[1]pg 23 is an analog of a homotopy between topological spaces for simplicial sets. If
- [math]\displaystyle{ f, g: X \to Y }[/math]
are maps between simplicial sets, a simplicial homotopy from f to g is a map
- [math]\displaystyle{ h: X \times \Delta^{1} \to Y }[/math]
such that the diagram (see [1]) formed by f, g and h commute; the key is to use the diagram that results in [math]\displaystyle{ f(x) = h(x, 0) }[/math] and [math]\displaystyle{ g(x) = h(x, 1) }[/math] for all x in X.
See also
- Kan complex
- Dold–Kan correspondence (under which a chain homotopy corresponds to a simplicial homotopy)
- Simplicial homology
References
- ↑ Goerss, Paul G.; Jardin, John F. (2009). Simplicial Homotopy Theory. Birkhäuser Basel. ISBN 978-3-0346-0188-7. OCLC 837507571. http://worldcat.org/oclc/837507571.
External links
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