Difference between revisions of "SET (category)"
From Maths
m (Alec moved page SETS (category) to SET (category) without leaving a redirect: It should be SET not SETS (I will create a redirect)) |
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==Definition== | ==Definition== | ||
| − | The [[category]] {{M|\mathrm{ | + | The [[category]] {{M|\mathrm{SET} }} is the category that contains every [[set]] for its [[objects of a category|objects]] and every [[function]] (in the conventional sense, as mappings from 1 set to another) between those sets as the [[arrows of a category|arrows of the category]]{{rAITCTHS2010}}. |
| + | * '''Note: ''' sometimes the {{M|\mathrm{SET} }} category is {{AKA}} {{M|\mathrm{SETS} }} (and the page <code>[[SETS (category)]]</code> redirects here) | ||
==[[Subcategory|Subcategories]]== | ==[[Subcategory|Subcategories]]== | ||
(Loads) | (Loads) | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
| + | {{Category theory navbox}} | ||
{{Definition|Category Theory}} | {{Definition|Category Theory}} | ||
[[Category:Examples of categories]] | [[Category:Examples of categories]] | ||
{{Example|Category Theory}} | {{Example|Category Theory}} | ||
Latest revision as of 10:05, 19 February 2016
Definition
The category [ilmath]\mathrm{SET} [/ilmath] is the category that contains every set for its objects and every function (in the conventional sense, as mappings from 1 set to another) between those sets as the arrows of the category[1].
- Note: sometimes the [ilmath]\mathrm{SET} [/ilmath] category is AKA [ilmath]\mathrm{SETS} [/ilmath] (and the page
SETS (category)redirects here)
Subcategories
(Loads)
- [ilmath]\mathrm{GROUP} [/ilmath] - the category of all groups and group homomorphisms
- [ilmath]\mathrm{AGROUP} [/ilmath] - a subcategory of [ilmath]\mathrm{GROUP} [/ilmath] consisting of all Abelian groups and their homomorphisms which are just the group homomorphisms between Abelian groups)
- [ilmath]\mathrm{TOP} [/ilmath] - the category of all topological spaces, the arrows are continuous maps
Many more, rings, commutative rings, so forth.
TODO: (More) exhaustive list
References
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