Definition:Monotone (Order Theory)/Mapping
< Definition:Monotone (Order Theory)(Redirected from Definition:Monotone Mapping)
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Definition
Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be ordered sets.
Let $\phi: \left({S, \preceq_1}\right) \to \left({T, \preceq_2}\right)$ be a mapping.
Then $\phi$ is monotone if and only if it is either increasing or decreasing.
Note that this definition also holds if $S = T$.
Also defined as
Some authors take monotone mapping to mean what on $\mathsf{Pr} \infty \mathsf{fWiki}$ is called an increasing mapping.
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): $\S 14$
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 1.4.3$