# Category:Definitions/Increasing Mappings

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This category contains definitions related to Increasing Mappings.

Related results can be found in Category:Increasing Mappings.

Let $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ be ordered sets.

Let $\phi: S \to T$ be a mapping.

Then $\phi$ is **increasing** if and only if:

- $\forall x, y \in S: x \preceq_1 y \implies \map \phi x \preceq_2 \map \phi y$

Note that this definition also holds if $S = T$.

## Also see

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Definitions/Increasing Mappings"

The following 11 pages are in this category, out of 11 total.