# Definition:Category of Rings

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## Definition

The **category of rings**, denoted $\mathbf{Ring}$, is the category with:

Objects: | rings | |

Morphisms: | ring homomorphisms | |

Composition: | composition of mappings | |

Identity morphisms: | identity mappings |

### Category of rings with unity

The **category of rings with unity** is the category with:

Objects: | rings with unity | |

Morphisms: | unital ring homomorphisms | |

Composition: | composition of mappings | |

Identity morphisms: | identity mappings |