See monic in All languages combined, or Wiktionary
Download JSON data for monic meaning in English (4.4kB)
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"2": "mono",
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"pos": "adj",
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"Of a polynomial whose leading coefficient is one."
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"(mathematics) Of a polynomial whose leading coefficient is one."
],
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"glosses": [
"Monomorphic."
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"biology",
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"Monomorphic",
"monomorphic"
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"raw_glosses": [
"(biology) Monomorphic."
],
"tags": [
"not-comparable"
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"topics": [
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{
"kind": "topical",
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"ref": "1995, Colin McLarty, “Introduction”, in Elementary Categories, Elementary Toposes, page 5",
"text": "It is often convenient to view a monic arrow i:A↣C, defined in Chapter 1, as showing that A is a copy of a part of C, and that i maps the copy on to that part. For example, in Set, the monic arrows are the one-to-one functions and, clearly, if i is one-to-one then A is a copy of a subset of C, namely of the image of i.",
"type": "quotation"
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{
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"Of a morphism: that it is a monomorphism."
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"monomorphism",
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"(category theory) Of a morphism: that it is a monomorphism."
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"word": "monic"
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{
"glosses": [
"A monic polynomial."
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"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "of a polynomial whose leading coefficient is one",
"word": "mònic"
},
{
"code": "fr",
"lang": "French",
"sense": "of a polynomial whose leading coefficient is one",
"word": "unitaire"
},
{
"code": "fr",
"lang": "French",
"sense": "of a polynomial whose leading coefficient is one",
"word": "normalisé"
},
{
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"lang": "Spanish",
"sense": "of a polynomial whose leading coefficient is one",
"tags": [
"masculine"
],
"word": "mónico"
}
]
}
],
"word": "monic"
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"(mathematics) Of a polynomial whose leading coefficient is one."
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"categories": [
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"Monomorphic."
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"biology",
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],
"raw_glosses": [
"(biology) Monomorphic."
],
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},
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"categories": [
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"examples": [
{
"ref": "1995, Colin McLarty, “Introduction”, in Elementary Categories, Elementary Toposes, page 5",
"text": "It is often convenient to view a monic arrow i:A↣C, defined in Chapter 1, as showing that A is a copy of a part of C, and that i maps the copy on to that part. For example, in Set, the monic arrows are the one-to-one functions and, clearly, if i is one-to-one then A is a copy of a subset of C, namely of the image of i.",
"type": "quotation"
},
{
"text": "If a composition (of morphisms) is monic then, by theorem, the pre-composite of it is monic as well."
}
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"Of a morphism: that it is a monomorphism."
],
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],
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"monomorphism",
"monomorphism"
]
],
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"(category theory) Of a morphism: that it is a monomorphism."
],
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"not-comparable"
],
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{
"glosses": [
"A monic polynomial."
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"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "of a polynomial whose leading coefficient is one",
"word": "mònic"
},
{
"code": "fr",
"lang": "French",
"sense": "of a polynomial whose leading coefficient is one",
"word": "unitaire"
},
{
"code": "fr",
"lang": "French",
"sense": "of a polynomial whose leading coefficient is one",
"word": "normalisé"
},
{
"code": "es",
"lang": "Spanish",
"sense": "of a polynomial whose leading coefficient is one",
"tags": [
"masculine"
],
"word": "mónico"
}
],
"word": "monic"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 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.
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