group object
analogue of the definition of a group inside an arbitrary category
| rdfs:label |
"group object"@en
|
|
skos:alt |
"internal group"@en
|
| schema:description |
"analogue of the definition of a group inside an arbitrary category"@en
|
|
schema:date |
"2026-09-23T19:58:53+00:00"^^xsd:dateTime |
| schema:version | 2548906628 |
| wikibase:identifiers | 6 |
| wikibase:sitelinks | 8 |
| wikibase:statements | 12 |
| p:P2534 | wd:statement/Q765994-e0b13fa1-42c7-73f6-0b2b-cc81957e5680 |
| p:P2579 | wd:statement/Q765994-5B198462-39A1-46DB-AB56-925C38406E82 |
| wd:statement/Q765994-f406f169-4405-a235-99e5-7689a29800bf | |
| p:P2581 | wd:statement/Q765994-E74EF9BF-E371-4B7C-93F7-0C5091D3DDF3 |
| p:P279 | wd:statement/Q765994-11ea27ff-4ae0-ba1a-ebfc-6bf021bdf656 |
| wd:statement/Q765994-bfb24ea4-4d73-0c68-ffe5-95cf3f587107 | |
| p:P4215 | wd:statement/Q765994-2d62e1b8-485d-8a22-6798-a032c35fe924 |
| p:P6104 | wd:statement/Q765994-37A6D745-4D23-4A40-B317-4236E28FEEFB |
| p:P6366 | wd:statement/Q765994-F040EDDA-76BB-49C6-803A-7B2246DD2606 |
| p:P646 | wd:statement/Q765994-12168402-A6F3-4A49-83C0-FE241509C0B0 |
| p:P7554 | wd:statement/Q765994-1f1053f7-483c-28e8-8eca-6b4eae591ee0 |
| p:P8417 | wd:statement/Q765994-b5f74df7-4972-58c5-f7f0-0157e42ccfa5 |
|
p:direct- |
<http:/ |
|
p:direct- |
<https:/ |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>m</mi><mo stretchy="false">:</mo><mi>G</mi><mo stretchy="false">×</mo><mi>G</mi><mo stretchy="false" accent="false">→</mo><mi>G</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>e</mi><mo stretchy="false">:</mo><mn>1</mn><mo stretchy="false" accent="false">→</mo><mi>G</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>i</mi><mo stretchy="false">:</mo><mi>G</mi><mo stretchy="false" accent="false">→</mo><mi>G</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>m</mi><mo stretchy="false">∘</mo><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">×</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>G</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>m</mi><mo stretchy="false">∘</mo><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>G</mi></mrow></msub><mo stretchy="false">×</mo><mi>m</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>m</mi><mo stretchy="false">∘</mo><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>G</mi></mrow></msub><mo stretchy="false">×</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msubsup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">p</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">j</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>G</mi><mo stretchy="false">×</mo><mn>1</mn></mrow></mrow></msubsup></mtd></mtr><mtr><mtd></mtd><mtd><mi>m</mi><mo stretchy="false">∘</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">×</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>G</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msubsup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">p</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">j</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">×</mo><mi>G</mi></mrow></mrow></msubsup></mtd></mtr><mtr><mtd></mtd><mtd><mi>m</mi><mo stretchy="false">∘</mo><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>G</mi></mrow></msub><mo stretchy="false">×</mo><mi>i</mi><mo stretchy="false">)</mo><mo stretchy="false">∘</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">g</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>G</mi></mrow></msub><mo stretchy="false">=</mo><mi>m</mi><mo stretchy="false">∘</mo><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">×</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>G</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">∘</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">g</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>G</mi></mrow></msub><mo stretchy="false">=</mo><mi>e</mi></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | category theory |
| group theory | |
| wdt:P2581 | "03330894n" |
| wdt:P279 | monoid object |
| internal category | |
| wdt:P4215 | "group object" |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "158425844" |
| wdt:P646 | "/m/0f0pz" |
| wdt:P7554 | "Group_object" |
| wdt:P8417 | "Group_object" |
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