# Category:Composite Mappings

This category contains results about Composite Mappings.

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 $f_1$.

Then the composite of $f_1$ and $f_2$ is defined and denoted as:

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

That is, the composite mapping $f_2 \circ f_1$ is defined as:

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

## Subcategories

This category has the following 7 subcategories, out of 7 total.