Category of vector spaces | Wikipedia audio article

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00:00:45 1 Properties
00:01:31 2 Example: the category of vector spaces
00:02:42 3 Generalizations
00:03:02 4 See also



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SUMMARY
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In algebra, given a ring R, the category of left modules over R is the category whose objects are all left modules over R and whose morphisms are all module homomorphisms between left R-modules. For example, when R is the ring of integers Z, it is the same thing as the category of abelian groups. The category of right modules is defined in a similar way.
Note: Some authors use the term module category for the category of modules; this term can be ambiguous since it could also refer to a category with a monoidal-category action.