Yoneda lemma
in category theory, a theorem that embeds a locally small category into a category of functors
| rdfs:label |
"Yoneda lemma"@en
|
|
skos:alt |
"Yoneda embedding"@en
|
| schema:description |
"in category theory, a theorem that embeds a locally small category into a category of functors"@en
|
|
schema:date |
"2026-10-12T20:22:46+00:00"^^xsd:dateTime |
| schema:version | 2556331988 |
| wikibase:identifiers | 5 |
| wikibase:sitelinks | 17 |
| wikibase:statements | 14 |
| p:P138 | wd:statement/Q320577-0ac1966d-4294-c34e-7cd3-11377f54e169 |
| p:P227 | wd:statement/Q320577-7940D93E-29D4-443A-A648-494FA1402138 |
| p:P2534 | wd:statement/Q320577-324c3616-4b7b-ea54-247d-269395dd7e90 |
| p:P2579 | wd:statement/Q320577-049D46EF-A0BE-434A-8183-2BAD1DD5A630 |
| p:P31 | wd:statement/Q320577-8609c90b-49d2-53f8-8592-ee2b66455ea8 |
| p:P4215 | wd:statement/Q320577-6f60db66-4925-b848-7103-20535e5257a5 |
| p:P5555 | wd:statement/Q320577-0516db52-459f-46bc-4179-0b8b098c6e12 |
| p:P6104 | wd:statement/Q320577-36D767CC-2AE2-4246-87F6-EF61B4D30609 |
| p:P6366 | wd:statement/Q320577-19906AB5-A982-4BF5-A798-C269C554E3AF |
| p:P646 | wd:statement/Q320577-C810E581-1ADD-4093-B7FE-41C2A45860B7 |
| p:P6781 | wd:statement/Q320577-00baffad-4340-aa49-82af-c693de7e2568 |
| p:P7235 | wd:statement/Q320577-64525ac6-4116-6b94-a09e-4bd72035d00a |
| wd:statement/Q320577-6c24c0c6-40e7-4897-786e-43bb56144b41 | |
| wd:statement/Q320577-92852acd-4ca0-a08f-5ede-2f2122d97871 | |
|
p:direct- |
<https:/ |
|
p:direct- |
<https:/ |
| wdt:P138 | Nobuo Yoneda |
| wdt:P227 | "1350766518" |
| 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><msub><mi>hom</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi data-mjx-texclass="OP" mathvariant="normal">PSh</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></mrow></msub><mo stretchy="false">(</mo><msub><mi>hom</mi><mrow data-mjx-texclass="ORD"><mi>C</mi></mrow></msub><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo>,</mo><mi>c</mi><mo stretchy="false">)</mo><mo>,</mo><mi>X</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">≅</mo><mi>X</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">(</mo><mi>X</mi></mtd><mtd><mo stretchy="false">∈</mo><mi data-mjx-texclass="OP" mathvariant="normal">PSh</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><msub><mi>hom</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi data-mjx-texclass="OP" mathvariant="normal">PSh</mi><mo>⁡</mo><mo stretchy="false">(</mo><msup><mi>C</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-texclass="OP" mathvariant="normal">op</mi></mrow></msup><mo stretchy="false">)</mo></mrow></mrow></msub><mo stretchy="false">(</mo><msub><mi>hom</mi><mrow data-mjx-texclass="ORD"><mi>C</mi></mrow></msub><mo stretchy="false">(</mo><mi>c</mi><mo>,</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo><mo>,</mo><mi>X</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">≅</mo><mi>X</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">(</mo><mi>X</mi></mtd><mtd><mo stretchy="false">∈</mo><mi data-mjx-texclass="OP" mathvariant="normal">PSh</mi><mo>⁡</mo><mo stretchy="false">(</mo><msup><mi>C</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-texclass="OP" mathvariant="normal">op</mi></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | category theory |
| wdt:P31 | theorem |
| wdt:P4215 | "Yoneda lemma" |
| wdt:P5555 |
<http:/ |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "2780771819" |
| wdt:P646 | "/m/088bx" |
| wdt:P6781 | "Yoneda_Lemma" |
| wdt:P7235 | "<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"><mi data-mjx-texclass="OP" mathvariant="normal">PSh</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<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"><mi>C</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<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"><msub><mi>hom</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi data-mjx-texclass="OP" mathvariant="normal">Psh</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></mrow></msub></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
Download as: