functor

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func·tor

(fŭngk′tər)
n.
1. One that performs an operation or a function.
2. Grammar See function word.

[New Latin fūnctor, from Latin fūnctiō, performance, function; see function.]

functor

(ˈfʌŋktə)
n
1. (Grammar) (in grammar) a function word or form word
2. (Mathematics) (in mathematics) a function that maps elements of one set to those of another

func•tor

(ˈfʌŋk tər)

n.
that which functions; operator.
[1935–40]
Translations
Funktor
funktori
funktor
funktor
funktor
Mentioned in ?
References in periodicals archive ?
The authorsAE approach to rigid geometry allows formal algebraic spaces, not only formal schemes, to be formal models of rigid spaces, and treats non-Noetherian formal schemes over an ?-adically complete valuation ring of arbitrary height for reasons of functoriality. Distributed in the US by the American Mathematical Society.
Then, by functoriality, Proposition 23 holds, where [mathematical expression not reproducible].
Topology deals with this problem via the concept of functoriality which is used to compute the topological invariants from discrete approximations.
Gillespie, Superposition of Zeroes of Automorphic L-Functions and Functoriality, Univ.
"Functoriality and Grammatical Role in Syllogisms".
By functoriality of the n we get homomorphisms [i.sub.*] : [[product].sub.n] [A, [x.sub.0]] [right arrow] [[product].sub.n] [G, [x.sub.0]] and [j.sub.*] : [[product].sub.n][G, [x.sub.0]] [right arrow] [[product].sub.n] [G, A, [x.sub.0]] for n [greater than or equal to] 2; [i.sub.*] is also a homomorphism when n = 1, We define a boundary operator [partial derivative]: [[product].sub.n+1] [G, A, [x.sub.0] [right arrow] [[product].sub.n] [A, [x.sub.0]] as follows: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [gamma] : ([I.sup.n+1], [I.sup.n], 0)[right arrow](G,A,[x.sub.0]) is an element of [Q.sup.n+1](G, A, [x.sub.0]) We get a long homotopy sequence:
The proof of functoriality of K is left as an exercise for the reader.
Among the topics are the functoriality of Rieffel's generalized fixed-point algebras for proper actions, division algebras and supersymmetry, Riemann-Roch and index formulae in twisted K-theory, noncommutative Yang-Mills theory for quantum Heisenberg manifolds, distances between matrix algebras that converge to coadjoint orbits, and geometric and topological structures related to M-branes.
By functoriality F([i.sup.-1]) and Gi are both isomorphisms, where [i.sup.-1] is the isomorphism inverse to i.
Since [H.sup.2](U,L) = 0 for any affine open subscheme U of X and because of functoriality we could write [[symmetry].sub.x[element of][absolute value of X]] and in fact [[symmetry].sub.x[element of][absolute value of X\U]] instead of [[Pi].sub.x[element of][absolute value of X]].
Among their topics are some notations related to Langlands functoriality, unramified correspondence, formation of the main result in the even case, and Eisenstein series.
The Langlands Program and base change, one of the most studied manifestations of the principle of functoriality, provides a concrete example of the interaction between arithmetic and C*-algebras.

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