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 |