# Definition:Category of Pointed Sets

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## Definition

The **category of pointed sets**, denoted $\mathbf {Set}_*$, is defined as follows:

Objects: | pointed sets $\struct {A, a}$ | |

Morphisms: | pointed mappings | |

Composition: | Standard composition of mappings | |

Identity morphisms: | $\map {\mathrm {id}_{\struct {A, a} } } := \mathrm {id}_A$, the identity mapping on $A$ |

## Also see

- Results about
**the category of pointed sets**can be found here.

## Sources

- 2010: Steve Awodey:
*Category Theory*(2nd ed.) ... (previous) ... (next): $\S 1.6$: Example $1.8$