# Category:Definitions/Composite Mappings

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This category contains definitions related to Composite Mappings.

Related results can be found in Category:Composite Mappings.

Let $S_1$, $S_2$ and $S_3$ be sets.

Let $f_1: S_1 \to S_2$ and $f_2: S_2 \to S_3$ be mappings such that the domain of $f_2$ is the same set as the codomain of $f_1$.

### Definition 1

The **composite mapping** $f_2 \circ f_1$ is defined as:

- $\forall x \in S_1: \map {\paren {f_2 \circ f_1} } x := \map {f_2} {\map {f_1} x}$

### Definition 2

The **composite of $f_1$ and $f_2$** is defined and denoted as:

- $f_2 \circ f_1 := \set {\tuple {x, z} \in S_1 \times S_3: \tuple {\map {f_1} x, z} \in f_2}$

### Definition 3

The **composite of $f_1$ and $f_2$** is defined and denoted as:

- $f_2 \circ f_1 := \set {\tuple {x, z} \in S_1 \times S_3: \exists y \in S_2: \map {f_1} x = y \land \map {f_2} y = z}$

## Pages in category "Definitions/Composite Mappings"

The following 9 pages are in this category, out of 9 total.

### C

- Definition:Composition of Mappings
- Definition:Composition of Mappings/Also known as
- Definition:Composition of Mappings/Binary Operation
- Definition:Composition of Mappings/Commutative Diagram
- Definition:Composition of Mappings/Definition 1
- Definition:Composition of Mappings/Definition 2
- Definition:Composition of Mappings/Definition 3
- Definition:Composition of Mappings/General Definition
- Definition:Composition of Mappings/Warning