functorn.

Brit.

/ˈfʌŋ(k)tə/, U.S.

/ˈfəŋ(k)tər/

Origin: Formed within English, by derivation. Etymons: function n., -or suffix.

Etymology: < funct- (in function n.) + -or suffix.In sense 1 after German Funktor (1934 in the passage translated in quot. 1937).

1. Logic. Originally: a symbol used to express a given relationship between numerical values. In later use more generally: a symbol which can be applied to a predicate to yield another predicate; more fully predicate functor.

ΘΚΠ

the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > propositional function

predicate1903

propositional function1903

statement form1931

functor1937

1937 A. Smeaton tr. R. Carnap Logical Syntax Lang. §3. p. 14 In order to express properties or relations of position by means of numbers, we shall use functors [Ger. Funktoren].

1951 J. Łukasiewicz Aristotle's Syllogistic iv. 78 The principle of my notation is to write the functors before the arguments. In this way I can avoid brackets.

1971 W. V. Quine in J. E. Fenstad Proc. 2nd Scandinavian Logic Symposium (Stud. Logic & Foundations Math. vol. 63) 311 There are six functors on predicates, and one constant two-place predicate.

1981 Jrnl. Symbolic Logic 46 649 Quantification theory..can be formulated in terms purely of predicate letters and a few predicate functors.

2009 Philos. Q. 59 269 I use the functors defined in Quine's original paper.

2. Mathematics. A mapping from one category (category n. Additions 3) to another which assigns to each object and morphism in the first category an object and morphism in the second, subject to certain conditions.Functors are typically classified as either covariant or contravariant. The criteria for a mapping F between two categories to be a covariant functor are that: if f: X → Y is a morphism in the first category, then F( f ) is a morphism from F( X ) to F( Y ); the identity morphism of the first category is mapped to that of the second; and the mapping preserves composition of morphisms. Using the same notation as above, the criteria for a mapping to be a contravariant functor is almost identical, the only differences being that F ( f ) is a morphism from F( Y ) to F ( X ), and the order of composition of morphisms is reversed—e.g. if ∘ represents the operation of composition, then F( f∘g) = F( g )∘F( f ).Unless otherwise specified, ‘functor’ used without a distinguishing word typically refers to a covariant functor.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > other

adjunction1891

homotopy1918

functor1942

1942 S. MacLane & S. Eilenberg in Proc. National Acad. Sci. U.S.A 28 538 The functions..jointly form what we shall call a ‘functor’, in this case, a ‘contravariant’ one.

1961 Mathematische Annalen 144 364 The following five formulas are valid for any covariant functors.

1975 Econometrica 43 432 A contravariant functor..is constructed as follows.

2014 D. I. Spivak Category Theory for Sci. v. 285 To describe a functor, we need to say what it does on objects..and what it does on morphisms.

3. Linguistics. A word or affix whose primary purpose is to contribute to the syntax rather than the meaning of a sentence; = function word n. at function n. Compounds.

ΘΚΠ

the mind > language > linguistics > study of grammar > a part of speech > [noun] > function word

particle1533

parcel1571

syncategorem1655

agency1778

empty word1854

symbolic1871

form-word1875

structural word1884

particule1889

pheme1906

structure word1925

function word1927

operator1938

logical word1940

keneme1950

rheme1953

functor1958

1958 C. F. Hockett Course in Mod. Linguistics xxxi. 264 There are at least three types of grammatical forms which are to be classed as functors.

1965 Listener 17 June 903/2 In themselves prepositions (which may be described as structure-words or functors) have no lexical meanings.

1995 Appl. Linguistics 16 197 Examples of children's neologisms which are the result of fusion, including the lexicalization of syntactic strings where grammatical functors have been removed (a down-to-the-floor dress→a down-floor dress).

2008 Mod. Lang. Jrnl. 92 238/1 Third-person present -s and possessive -s are the last acquired functors in the morpheme order studies.

Derivatives

funcˈtorial adj.

ΘΚΠ

the mind > mental capacity > philosophy > logic > predicate or propositional logic > [adjective] > of a function, operator, or variable

predicative1906

unary1931

inclusive1940

one-argument1941

functorial1945

1945 Trans. Amer. Math. Soc. 58 292 This category X_b would be used in a functorial treatment of the fundamental group and of the homotopy groups.

1951 J. Łukasiewicz Aristotle's Syllogistic v. 132 All these may be called functorial propositions, since in all of them there occurs a propositional functor, like ‘if—then’, ‘or’, ‘and’.

2014 C. F. Nourani Functorial Model Theory p. ix This book is a preliminary introduction to a functorial model theory based on infinitary language categories.

This entry has been updated (OED Third Edition, September 2017; most recently modified version published online March 2022).

单词	functor
释义	functorn. Brit. /ˈfʌŋ(k)tə/, U.S. /ˈfəŋ(k)tər/ Origin: Formed within English, by derivation. Etymons: function n., -or suffix. Etymology: < funct- (in function n.) + -or suffix.In sense 1 after German Funktor (1934 in the passage translated in quot. 1937). 1. Logic. Originally: a symbol used to express a given relationship between numerical values. In later use more generally: a symbol which can be applied to a predicate to yield another predicate; more fully predicate functor. ΘΚΠ the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > propositional function predicate1903 propositional function1903 statement form1931 functor1937 1937 A. Smeaton tr. R. Carnap Logical Syntax Lang. §3. p. 14 In order to express properties or relations of position by means of numbers, we shall use functors [Ger. Funktoren]. 1951 J. Łukasiewicz Aristotle's Syllogistic iv. 78 The principle of my notation is to write the functors before the arguments. In this way I can avoid brackets. 1971 W. V. Quine in J. E. Fenstad Proc. 2nd Scandinavian Logic Symposium (Stud. Logic & Foundations Math. vol. 63) 311 There are six functors on predicates, and one constant two-place predicate. 1981 Jrnl. Symbolic Logic 46 649 Quantification theory..can be formulated in terms purely of predicate letters and a few predicate functors. 2009 Philos. Q. 59 269 I use the functors defined in Quine's original paper. 2. Mathematics. A mapping from one category (category n. Additions 3) to another which assigns to each object and morphism in the first category an object and morphism in the second, subject to certain conditions.Functors are typically classified as either covariant or contravariant. The criteria for a mapping F between two categories to be a covariant functor are that: if f: X → Y is a morphism in the first category, then F( f ) is a morphism from F( X ) to F( Y ); the identity morphism of the first category is mapped to that of the second; and the mapping preserves composition of morphisms. Using the same notation as above, the criteria for a mapping to be a contravariant functor is almost identical, the only differences being that F ( f ) is a morphism from F( Y ) to F ( X ), and the order of composition of morphisms is reversed—e.g. if ∘ represents the operation of composition, then F( f∘g) = F( g )∘F( f ).Unless otherwise specified, ‘functor’ used without a distinguishing word typically refers to a covariant functor. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > other adjunction1891 homotopy1918 functor1942 1942 S. MacLane & S. Eilenberg in Proc. National Acad. Sci. U.S.A 28 538 The functions..jointly form what we shall call a ‘functor’, in this case, a ‘contravariant’ one. 1961 Mathematische Annalen 144 364 The following five formulas are valid for any covariant functors. 1975 Econometrica 43 432 A contravariant functor..is constructed as follows. 2014 D. I. Spivak Category Theory for Sci. v. 285 To describe a functor, we need to say what it does on objects..and what it does on morphisms. 3. Linguistics. A word or affix whose primary purpose is to contribute to the syntax rather than the meaning of a sentence; = function word n. at function n. Compounds. ΘΚΠ the mind > language > linguistics > study of grammar > a part of speech > [noun] > function word particle1533 parcel1571 syncategorem1655 agency1778 empty word1854 symbolic1871 form-word1875 structural word1884 particule1889 pheme1906 structure word1925 function word1927 operator1938 logical word1940 keneme1950 rheme1953 functor1958 1958 C. F. Hockett Course in Mod. Linguistics xxxi. 264 There are at least three types of grammatical forms which are to be classed as functors. 1965 Listener 17 June 903/2 In themselves prepositions (which may be described as structure-words or functors) have no lexical meanings. 1995 Appl. Linguistics 16 197 Examples of children's neologisms which are the result of fusion, including the lexicalization of syntactic strings where grammatical functors have been removed (a down-to-the-floor dress→a down-floor dress). 2008 Mod. Lang. Jrnl. 92 238/1 Third-person present -s and possessive -s are the last acquired functors in the morpheme order studies. Derivatives funcˈtorial adj. ΘΚΠ the mind > mental capacity > philosophy > logic > predicate or propositional logic > [adjective] > of a function, operator, or variable predicative1906 unary1931 inclusive1940 one-argument1941 functorial1945 1945 Trans. Amer. Math. Soc. 58 292 This category X_b would be used in a functorial treatment of the fundamental group and of the homotopy groups. 1951 J. Łukasiewicz Aristotle's Syllogistic v. 132 All these may be called functorial propositions, since in all of them there occurs a propositional functor, like ‘if—then’, ‘or’, ‘and’. 2014 C. F. Nourani Functorial Model Theory p. ix This book is a preliminary introduction to a functorial model theory based on infinitary language categories. This entry has been updated (OED Third Edition, September 2017; most recently modified version published online March 2022). < n.1937
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