See functor on Wiktionary
Download JSON data for functor meaning in All languages combined (14.8kB)
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"text": "Given a homotopical category X and a functor u#x3A;A#x5C;rightarrowB, a homotopical u-colimit (resp. u-limit) functor on X will be a homotopically terminal (resp. initial) Kan extension of the identity (50.2) along the induced diagram functor Xᵘ#x3A;Xᴮ#x5C;rightarrowXᴬ (47.1).",
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"text": "2009, Benoit Fresse, Modules Over Operads and Functors, Springer, Lecture Notes in Mathematics: 1967, page 35,\nIn this chapter, we recall the definition of the category of Σ_*-objects and we review the relationship between Σ_*-objects and functors. In short, a Σ_*-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor S(M):X→S(M,X), defined by a formula of the form\nS(M,X)=⨁ ᪲ᵣ₌₀(M(r)⊗X)_(Σᵣ)."
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{
"ref": "2004, William G. Dwyer, Philip S. Hirschhorn, Daniel M. Kan, Jeffrey H. Smith, Homotopy Limit Functors on Model Categories and Homotopical Categories, American Mathematical Society, page 165",
"text": "Given a homotopical category X and a functor u#x3A;A#x5C;rightarrowB, a homotopical u-colimit (resp. u-limit) functor on X will be a homotopically terminal (resp. initial) Kan extension of the identity (50.2) along the induced diagram functor Xᵘ#x3A;Xᴮ#x5C;rightarrowXᴬ (47.1).",
"type": "quotation"
},
{
"text": "2009, Benoit Fresse, Modules Over Operads and Functors, Springer, Lecture Notes in Mathematics: 1967, page 35,\nIn this chapter, we recall the definition of the category of Σ_*-objects and we review the relationship between Σ_*-objects and functors. In short, a Σ_*-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor S(M):X→S(M,X), defined by a formula of the form\nS(M,X)=⨁ ᪲ᵣ₌₀(M(r)⊗X)_(Σᵣ)."
}
],
"glosses": [
"A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities."
],
"links": [
[
"category theory",
"category theory"
],
[
"category",
"category"
],
[
"homomorphism",
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],
[
"morphism",
"morphism"
],
[
"covariant",
"covariant"
],
[
"contravariant",
"contravariant"
],
[
"composition",
"composition"
],
[
"identities",
"identity"
]
],
"raw_glosses": [
"(category theory) A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities."
],
"topics": [
"category-theory",
"computing",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
]
},
{
"categories": [
"en:Programming"
],
"glosses": [
"A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory."
],
"links": [
[
"functional programming",
"functional programming"
],
[
"function",
"function"
],
[
"generic type",
"generic type"
]
],
"qualifier": "functional programming",
"raw_glosses": [
"(functional programming) A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory."
]
}
],
"sounds": [
{
"ipa": "/ˈfʌŋktə/",
"tags": [
"Received-Pronunciation"
]
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "object-oriented programming: function object",
"word": "funktio-olio"
},
{
"code": "fr",
"lang": "French",
"sense": "object-oriented programming: function object",
"tags": [
"masculine"
],
"word": "foncteur"
},
{
"code": "ba",
"lang": "Bashkir",
"roman": "funktor",
"sense": "category theory: category mapping",
"word": "функтор"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "hánzǐ",
"sense": "category theory: category mapping",
"word": "函子"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "category theory: category mapping",
"word": "funktori"
},
{
"code": "fr",
"lang": "French",
"sense": "category theory: category mapping",
"tags": [
"masculine"
],
"word": "foncteur"
},
{
"code": "de",
"lang": "German",
"sense": "category theory: category mapping",
"tags": [
"masculine"
],
"word": "Funktor"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "category theory: category mapping",
"word": "funktor"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "category theory: category mapping",
"tags": [
"masculine"
],
"word": "varpi"
},
{
"code": "ga",
"lang": "Irish",
"sense": "category theory: category mapping",
"word": "feidhmeoir"
},
{
"code": "it",
"lang": "Italian",
"sense": "category theory: category mapping",
"tags": [
"masculine"
],
"word": "funtore"
},
{
"alt": "かんしゅ",
"code": "ja",
"lang": "Japanese",
"roman": "kanshu",
"sense": "category theory: category mapping",
"word": "関手"
},
{
"code": "kk",
"lang": "Kazakh",
"roman": "funktor",
"sense": "category theory: category mapping",
"word": "функтор"
},
{
"code": "ky",
"lang": "Kyrgyz",
"roman": "funktor",
"sense": "category theory: category mapping",
"word": "функтор"
},
{
"code": "pl",
"lang": "Polish",
"sense": "category theory: category mapping",
"tags": [
"masculine"
],
"word": "funktor"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "category theory: category mapping",
"tags": [
"masculine"
],
"word": "functor"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "category theory: category mapping",
"tags": [
"masculine"
],
"word": "funtor"
},
{
"code": "ru",
"lang": "Russian",
"roman": "funktor",
"sense": "category theory: category mapping",
"word": "функтор"
},
{
"code": "es",
"lang": "Spanish",
"sense": "category theory: category mapping",
"tags": [
"masculine"
],
"word": "funtor"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "category theory: category mapping",
"tags": [
"common-gender"
],
"word": "funktor"
}
],
"word": "functor"
}
{
"forms": [
{
"form": "functores",
"tags": [
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]
}
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"args": {
"1": "m"
},
"expansion": "functor m (plural functores)",
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}
],
"lang": "Portuguese",
"lang_code": "pt",
"pos": "noun",
"senses": [
{
"categories": [
"Portuguese countable nouns",
"Portuguese entries with incorrect language header",
"Portuguese lemmas",
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"Portuguese nouns",
"Portuguese nouns with red links in their headword lines",
"pt:Category theory"
],
"glosses": [
"functor (a mapping between categories)"
],
"links": [
[
"category theory",
"category theory"
],
[
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]
],
"raw_glosses": [
"(category theory) functor (a mapping between categories)"
],
"tags": [
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],
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"natural-sciences",
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]
}
],
"synonyms": [
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"word": "funtor"
}
],
"word": "functor"
}
{
"etymology_templates": [
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},
"expansion": "Borrowed",
"name": "glossary"
},
{
"args": {
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"2": "fr",
"3": "functeur",
"4": "",
"5": "",
"g": "",
"g2": "",
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"id": "",
"lit": "",
"nocat": "",
"pos": "",
"sc": "",
"sort": "",
"tr": "",
"ts": ""
},
"expansion": "French functeur",
"name": "bor"
},
{
"args": {
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"2": "fr",
"3": "functeur"
},
"expansion": "Borrowed from French functeur",
"name": "bor+"
}
],
"etymology_text": "Borrowed from French functeur.",
"forms": [
{
"form": "functori",
"tags": [
"plural"
]
},
{
"form": "no-table-tags",
"source": "declension",
"tags": [
"table-tags"
]
},
{
"form": "ro-noun-m",
"source": "declension",
"tags": [
"inflection-template"
]
},
{
"form": "functor",
"source": "declension",
"tags": [
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"indefinite",
"nominative",
"singular"
]
},
{
"form": "un functor",
"source": "declension",
"tags": [
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"indefinite",
"nominative",
"singular"
]
},
{
"form": "functorul",
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"tags": [
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"definite",
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"singular"
]
},
{
"form": "functori",
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"tags": [
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},
{
"form": "niște functori",
"source": "declension",
"tags": [
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"indefinite",
"nominative",
"plural"
]
},
{
"form": "functorii",
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"tags": [
"accusative",
"definite",
"nominative",
"plural"
]
},
{
"form": "functor",
"source": "declension",
"tags": [
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"genitive",
"indefinite",
"singular"
]
},
{
"form": "unui functor",
"source": "declension",
"tags": [
"dative",
"genitive",
"indefinite",
"singular"
]
},
{
"form": "functorului",
"source": "declension",
"tags": [
"dative",
"definite",
"genitive",
"singular"
]
},
{
"form": "functori",
"source": "declension",
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]
},
{
"form": "unor functori",
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"genitive",
"indefinite",
"plural"
]
},
{
"form": "functorilor",
"source": "declension",
"tags": [
"dative",
"definite",
"genitive",
"plural"
]
},
{
"form": "functorule",
"source": "declension",
"tags": [
"singular",
"vocative"
]
},
{
"form": "functorilor",
"source": "declension",
"tags": [
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]
}
],
"head_templates": [
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"2": "functori"
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"inflection_templates": [
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"args": {
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"gpi": "functori",
"gsd": "functorului",
"gsi": "functor",
"n": "",
"npd": "functorii",
"npi": "functori",
"nsd": "functorul",
"nsi": "functor",
"vp": "functorilor",
"vs": "functorule",
"vs2": ""
},
"name": "ro-decl-noun"
}
],
"lang": "Romanian",
"lang_code": "ro",
"pos": "noun",
"senses": [
{
"categories": [
"Romanian countable nouns",
"Romanian entries with incorrect language header",
"Romanian lemmas",
"Romanian masculine nouns",
"Romanian nouns",
"Romanian nouns with red links in their headword lines",
"Romanian terms borrowed from French",
"Romanian terms derived from French"
],
"glosses": [
"functor"
],
"links": [
[
"functor",
"functor#English"
]
],
"tags": [
"masculine"
]
}
],
"word": "functor"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.