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Mathematical functor in representation theory and algebraic topology
particularly in representation theory and algebraic topology, a Mackey functor is a type of functor that generalizes various constructions in group theory and
Mackey_functor
Category theory
is an additive category, then a C-valued Mackey functor is an additive functor from A(G) to C. Mackey functors are important in representation theory and
Burnside_category
Generalization of a category
Stable infinity category ∞-groupoid Higher category theory Globular set Mackey functor (∞, n)-category Homotopy coherent nerve Localization of an ∞-category
Quasi-category
American mathematician
George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician known for his contributions to quantum logic, representation theory
George_Mackey
Every Boolean algebra is isomorphic to a certain field of sets
other words, there is a contravariant functor that gives an equivalence between the categories. The inverse functor's action on morphisms maps a continuous
Stone's representation theorem for Boolean algebras
Stone's_representation_theorem_for_Boolean_algebras
Nigerian mathematician and academic (1941–2022)
rings and articulating higher algebraic K-theory in the language of Mackey functors. His work on equivariant higher algebraic K-theory and its generalisations
Aderemi_Kuku
Process of extending a representation of a subgroup to the parent group
respectively. With the addition of the normalizing factors this induction functor takes unitary representations to unitary representations. One other variation
Induced_representation
Category whose objects are representations and whose morphisms are equivariant maps
from the category of representations of it together with the forgetful functor to the category of vector spaces. The Grothendieck ring of the category
Category_of_representations
"Mackey machine" or "Mackey normal subgroup analysis". From the point of view of category theory, restriction is an instance of a forgetful functor. This
Restricted_representation
Operator encoding information about iterated map
pushforward of g: in essence, the transfer operator is the direct image functor in the category of measurable spaces. The left-adjoint of the Perron–Frobenius
Transfer_operator
Group homomorphism into the general linear group over a vector space
an arbitrary category C, a representation of G in C is a functor from G to C. Such a functor selects an object X in C and a group homomorphism from G
Group_representation
Mathematical relation in abstract algrebra
Similarly, for NG the co-induced representation of N from H to G using the Hom functor, and for H ∗ {\displaystyle \ast } the group cohomology: H ∗ {\displaystyle
Shapiro's_lemma
such that π {\displaystyle \pi } is injective as a function. fiber functor fiber functor. Frobenius reciprocity The Frobenius reciprocity states that for
Glossary of representation theory
Glossary_of_representation_theory
Branch of mathematics that studies abstract algebraic structures
be viewed as particular kinds of categories, and the representations as functors from the object category to the category of vector spaces. This description
Representation_theory
Representations of finite groups, particularly on vector spaces
of G. More precisely, for such a collection of subgroups, the induction functor yields a map φ : Ind : ⨁ H ∈ X R ( H ) → R ( G ) {\displaystyle \varphi
Representation theory of finite groups
Representation_theory_of_finite_groups
MACKEY FUNCTOR
MACKEY FUNCTOR
Boy/Male
French, German
Little Hacker; Little Hewer of Wood
Female
English
Variant spelling of English Marlie, MARLEY means "rebel of Magdala."Â
Surname or Lastname
English
English : habitational name from Markly in Heathfield, Sussex.
Female
English
English surname transferred to unisex forename use, from a variant form of the surname Massey which was originally a pet form of Matthew, MACEY means "gift of God."
Boy/Male
French
Of Mars; the god of war.
Male
Polish
Polish form of Greek Mattathias, MACIEJ means "gift of God."
Surname or Lastname
English
English : habitational name from any of various minor places called Matley, in particular Matley in Greater Manchester, Matley Heath and Matley Wood in Hampshire, or Matley Moor in Derbyshire.
Male
Russian
(Матвей) Russian form of Greek Mattathias, MATVEY means "gift of God."
Male
English
English surname transferred to unisex forename use, from a variant spelling of the surname Massey which was originally a pet form of Matthew, MACEY means "gift of God."
Boy/Male
Hebrew American English Irish
Who is like God? Gift from God. In the Bible, St. Michael was the conqueror of Satan and patron...
Boy/Male
German
Little hacker.
Male
English
Unisex pet form of English Michael and Michaela, both MICKEY means "who is like God?"
Surname or Lastname
English (Cornwall)
English (Cornwall) : habitational name from Mankea in Cornwall, named with Corinsh men ‘stone’ + kee ‘bank’, ‘hedge’.Americanized form of German Manke.
Boy/Male
American, Australian, British, Chinese, Danish, English, French, Hebrew, Irish
Who is Like God; Form of Michael; Diminutive Form of Michael Like God
Surname or Lastname
English
English : topographic name for someone who lived by a market, Middle English market.
Boy/Male
Australian, Scottish
Son of Fire
Surname or Lastname
English
English : habitational name from Mackley in Derbyshire, which may have been named in Old English as ‘Macca’s forest’, from an unattested personal name + lēah ‘woodland clearing’, ‘glade’.Scottish : Anglicized form of Gaelic Mac Donnshleibhe ‘son of Donnshleibhe’, a personal name literally meaning ‘brown hill’.Probably also an Americanized form of German Mä(g)gli (see Magley).
Male
English
Contracted form of English Ackerley, ACKLEY means "oak meadow."
Male
Welsh
Welsh form of Latin Maxim, MACSEN means "the greatest rival."Â
Surname or Lastname
English
English : probably a topographic name for someone living in the Lickey Hills, southwest of Birmingham.Perhaps an altered spelling of Scottish Leckie.
MACKEY FUNCTOR
MACKEY FUNCTOR
Boy/Male
Australian, German, Hungarian
Name of a Honour; Youth
Boy/Male
Australian, French, Italian, Latin, Portuguese
From Nazareth
Boy/Male
Gujarati, Indian, Sanskrit
One who is Far Away with Worthless Affection; Free from Illusion; Undeluded
Surname or Lastname
English
English : variant of Roke, a topographic name for someone who lived near an oak tree (see Oak), from a misdivision of Middle English atter oke ‘at the oak’. Roke in Oxfordshire and Rock in Worcestershire are named in this way, and so the surname may be habitational in some cases.English : possibly a variant of Rock 1.
Girl/Female
American, Australian, British, English
White Wave; Variant of Jenny which is a Diminutive of Jane and Jennifer
Boy/Male
Hindu
Reliever of sorrows
Surname or Lastname
English
English : unexplained.
Boy/Male
Tamil
Symbol, First word in a sentence
Girl/Female
Greek American English Latin
Christian.
Girl/Female
Hindu, Indian, Kannada
Protection in the Name of God
MACKEY FUNCTOR
MACKEY FUNCTOR
MACKEY FUNCTOR
MACKEY FUNCTOR
MACKEY FUNCTOR
v. t.
To attend as a lackey; to wait upon.
a.
Marked like macle (chiastolite).
n.
Exchange, or purchase and sale; traffic; as, a dull market; a slow market.
n.
The price for which a thing is sold in a market; market price. Hence: Value; worth.
a.
Let out for hire; devoted to common use; hence, much used; trite; mean; as, hackney coaches; hackney authors.
v. i.
To make a confused noise or racket.
a.
Having a back; fitted with a back; as, a backed electrotype or stereotype plate. Used in composition; as, broad-backed; hump-backed.
v. t.
To play the jockey toward; to cheat; to trick; to impose upon in trade; as, to jockey a customer.
a.
Rough or broken, as if hacked.
v. i.
To deal in a market; to buy or sell; to make bargains for provisions or goods.
v. t.
To put a jacket on; to furnish, as a boiler, with a jacket.
v. i.
To play or act the jockey; to cheat.
v. t.
To make up into a packet or bundle.
v. t.
To carry in a hackney coach.
a.
Designated or distinguished by, or as by, a mark; hence; noticeable; conspicuous; as, a marked card; a marked coin; a marked instance.
pl.
of Lackey
a. & n.
See Tacky.
v. i.
To act or serve as lackey; to pay servile attendance.
n.
See Hockey.
v. t.
To strike with, or as with, a racket.