functorn.
/ˈfʌŋ(k)tə/, U.S. /ˈfəŋ(k)tər/ 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 Xb 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).
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n.1937