Category of groups: Difference between revisions
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* Its objects are [[groupprops:group|group]]s. | * Its objects are [[groupprops:group|group]]s. | ||
* Its morphisms are homomorphisms of groups. | * Its morphisms are [[groupprops:homomorphism of groups|homomorphisms of groups]]. | ||
* The identity morphism is defined as the identity map. | * The identity morphism is defined as the identity map. | ||
* Composition of morphisms is defined by function composition. | * Composition of morphisms is defined by function composition. | ||
Latest revision as of 00:03, 10 December 2008
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Definition
The category of groups, denoted or , is defined as follows:
- Its objects are groups.
- Its morphisms are homomorphisms of groups.
- The identity morphism is defined as the identity map.
- Composition of morphisms is defined by function composition.