Difference between revisions of "SET (category)"

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(Created page with "==Definition== The category {{M|\mathrm{SETS} }} is the category that contains every set for its objects and every function (in the conve...")
 
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==Definition==
 
==Definition==
The [[category]] {{M|\mathrm{SETS} }} 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}}.
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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}}.
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* '''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]]==
 
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(Loads)
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==References==
 
==References==
 
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<references/>
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{{Category theory navbox}}
 
{{Definition|Category Theory}}
 
{{Definition|Category Theory}}
 
[[Category:Examples of categories]]
 
[[Category:Examples of categories]]
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{{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)

Many more, rings, commutative rings, so forth.


TODO: (More) exhaustive list


References

  1. An Introduction to Category Theory - Harold Simmons - 1st September 2010 edition