# Category:Canonical Injections

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This category contains results about **Canonical Injections** in the context of **Abstract Algebra**.

Definitions specific to this category can be found in Definitions/Canonical Injections.

Let $\struct {S_1, \circ_1}$ and $\struct {S_2, \circ_2}$ be algebraic structures with identities $e_1, e_2$ respectively.

The following mappings:

- $\inj_1: \struct {S_1, \circ_1} \to \struct {S_1, \circ_1} \times \struct {S_2, \circ_2}: \forall x \in S_1: \map {\inj_1} x = \tuple {x, e_2}$

- $\inj_2: \struct {S_2, \circ_2} \to \struct {S_1, \circ_1} \times \struct {S_2, \circ_2}: \forall x \in S_2: \map {\inj_2} x = \tuple {e_1, x}$

are called the **canonical injections**.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Canonical Injections"

The following 7 pages are in this category, out of 7 total.