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Related to Covariant functor: Contravariant functor, Functors, Bifunctor


1. One that performs an operation or a function.
2. Grammar See function word.

[New Latin fūnctor, from Latin fūnctiō, performance, function; see function.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.


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
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014


(ˈfʌŋk tər)

that which functions; operator.
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
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The K-theory functor, a covariant functor from [C.sup.*] algebras to abelian groups, gives rise to a morphism [[lambda].sub.*] of abelian groups.
[14] A covariant functor from a category C to a category D consists of two maps (denoted by the same letter), a map F : Ob(C) [member of] Ob(D), and for any A, B [member of] Ob(C) a map F : H(A, B) [member of] H(F(A), F(B)), satisfying the conditions:
Indeed, applying the covariant functor [Ext.sub.G].sup.*]([[epsilon].sub.[chi]] - [cross product].sub.z] [Z.sub.[rho]]) to this diagram gives a commuting diagram with exact rows
Instead, we make A [??] kA into a covariant functor.
Recall from [6] that a covariant functor [mu]: C [right arrow] V between categories satisfying (J1)-(J4) axioms is called a modelization functor if it preserves weak equivalences, homotopy pullbacks and homotopy pushouts.
ii) If (G, A, [kappa]) is an algebraic 3-type, then [sub.2][H.sup.n] (G, A, [kappa]; *) is a covariant functor from the category of abelian groups to the category of abelian groups.