Category of groups: Difference between revisions
(New page: {{particular category}} ==Definition== The '''category of groups''', denoted <math>\operatorname{Group}</math> or <math>\operatorname{Grp}</math>, is defined as follows: * Its objects a...) |
No edit summary |
||
| Line 5: | Line 5: | ||
The '''category of groups''', denoted <math>\operatorname{Group}</math> or <math>\operatorname{Grp}</math>, is defined as follows: | The '''category of groups''', denoted <math>\operatorname{Group}</math> or <math>\operatorname{Grp}</math>, is defined as follows: | ||
* Its objects are [[group]]s. | * Its objects are [[groupprops:group|group]]s. | ||
* Its morphisms are homomorphisms of groups. | * Its morphisms are 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. | ||
==External links== | |||
===Other subject wikis=== | |||
* [[groupprops:category of groups|Groupprops, the group properties wiki]] | |||
Revision as of 00:02, 10 December 2008
This article is about a particular category
View other particular categories
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.