SHMARQL

functor

<http://www.wikidata.org/entity/Q864475>

in category theory, a mapping between categories that preserves their structure (identity morphisms, composition of morphisms)
functor
rdfs:label
"functor"@en
skos:altLabel
"contravariant functor"@en
"covariant functor"@en
schema:description
"in category theory, a mapping between categories that preserves their structure (identity morphisms, composition of morphisms)"@en
schema:dateModified "2026-08-14T12:08:26+00:00"^^xsd:dateTime
schema:version 2531303055
wikibase:identifiers 17
wikibase:sitelinks 29
wikibase:statements 33
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p:P10376 wd:statement/Q864475-ed9fb011-419c-d7b5-1f12-cb85b0fad744
p:P1051 wd:statement/Q864475-8EAD37C0-A83F-4776-BD05-0FF4A788C067
p:P1245 wd:statement/Q864475-4B3B2EC6-EC32-4E08-85DC-349E1D5B9BB4
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p:P1417 wd:statement/Q864475-B0827D9D-65B8-4403-B061-DAD40D673880
p:P14534 wd:statement/Q864475-71B978AC-6B75-4954-BF18-97C645AAF8DA
p:P18 wd:statement/Q864475-efb8e3a8-404d-6581-b6c2-37d75f49ab0b
p:P1889 wd:statement/Q864475-a5a22b22-49d8-3ae0-7ffd-836b40afa1e0
p:P1963 wd:statement/Q864475-507b6a41-40b6-564f-58be-80adf47a3189
wd:statement/Q864475-8406edc4-4e9f-3b77-5578-4aaea367dd7c
p:P2534 wd:statement/Q864475-d422369d-4612-911a-3024-8295296e881a
p:P2579 wd:statement/Q864475-2E1EC8BE-8045-4FA6-9D4F-4D1408DE665C
p:P279 wd:statement/Q864475-0edb0b73-415b-15a3-907e-f8aa2fc2da88
p:P2812 wd:statement/Q864475-9597e1be-45c9-2837-b3ff-961d96fd41df
p:P3365 wd:statement/Q864475-9dcb574b-4ab4-c219-8a8a-2041954b0bce
p:P3417 wd:statement/Q864475-8F098F10-2DCB-4C80-A749-35298EB39A6B
p:P361 wd:statement/Q864475-406be784-459f-2b91-79de-ba89ce811135
p:P373 wd:statement/Q864475-11FF3034-821F-456B-9AAB-A6CE18C53514
p:P3827 wd:statement/Q864475-BF354251-BA80-48BE-A74A-0E3CF8637316
p:P4215 wd:statement/Q864475-2A324C59-ED1F-44F8-ACF2-7274B04C5C4A
p:P61 wd:statement/Q864475-314d6830-41cb-5cbb-af94-7c316df31771
wd:statement/Q864475-a3edc4ce-4c22-5e85-5bd3-c232fe738479
p:P6104 wd:statement/Q864475-B7D10F41-0F54-4EAC-90F3-FEE2BB7119F7
p:P6366 wd:statement/Q864475-8A3EC781-00AD-4157-BDA2-B9DED42E6995
p:P646 wd:statement/Q864475-78D06625-A10D-4E2E-AF1E-5DE08F5FC438
p:P6781 wd:statement/Q864475-6455de75-49b2-ee74-e561-a7990fb53618
p:P7235 wd:statement/Q864475-669561f5-44a5-d53d-1d33-2abd541cbec0
wd:statement/Q864475-b4825f1c-4b59-0b4a-24fd-413aea0ca101
wd:statement/Q864475-c7325490-49e5-7473-1b45-7b443f0f6d07
p:P7554 wd:statement/Q864475-73b67e49-4e8c-4df7-ce01-73310d057ca7
p:P8408 wd:statement/Q864475-F0AC810B-3F6A-427E-B152-C8F344DBCE25
p:P910 wd:statement/Q864475-247A36C4-934B-4E6A-90DC-07370172BFB5
p:direct-normalized/P6366 <https://makg.org/entity/156772000>
p:direct-normalized/P8408 <http://kbpedia.org/kko/rc/Functor>
wdt:P10283 "C156772000"
wdt:P10376 "mathematics/functor"
wdt:P1051 "7364"
wdt:P1245 "955376"
wdt:P12888 "df-func"
wdt:P1417 "topic/functor"
wdt:P14534 "CategoryTheory.Functor"
wdt:P18 <http://commons.wikimedia.org/wiki/Special:FilePath/Commutative%20diagram%20of%20a%20functor.svg>
wdt:P1889 function object
wdt:P1963 definition domain
codomain
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><mi>F</mi><mo stretchy="false">(</mo><msub><mi data-mjx-texclass="OP" mathvariant="normal">id</mi><mrow data-mjx-texclass="ORD"><mi>X</mi></mrow></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo><msub><mi data-mjx-texclass="OP" mathvariant="normal">id</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>F</mi><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo></mrow></mrow></msub></mtd></mtr><mtr><mtd><mi>F</mi><mo stretchy="false">(</mo><mi>f</mi><mo stretchy="false">&#x2218;</mo><mi>g</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo><mi>F</mi><mi>f</mi><mo stretchy="false">&#x2218;</mo><mi>F</mi><mi>g</mi></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P2579 category theory
wdt:P279 semifunctor
wdt:P2812 "Functor"
wdt:P3365 "funtore"
wdt:P3417 "Functor-1"
wdt:P361 category theory
wdt:P373 "Functors"
wdt:P3827 "functors"
wdt:P4215 "functor"
wdt:P61 Saunders Mac Lane
Samuel Eilenberg
wdt:P6104 WikiProject Mathematics
wdt:P6366 "156772000"
wdt:P646 "/m/02yzn"
wdt:P6781 "Definition:Functor"
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">id</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"><mi>F</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"><mi>f</mi><mo stretchy="false">&#x2218;</mo><mi>g</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P7554 "Functor"
wdt:P8408 "Functor"
wdt:P910 Category:Functors
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