particularly in representation theory and algebraic topology, a Mackey functor is a type of functor that generalizes various constructions in group theory and...

George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician known for his contributions to quantum logic, representation 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...

Stable infinity category ∞-groupoid Higher category theory Globular set Mackey functor (∞, n)-category Homotopy coherent nerve Localization of an ∞-category...

respectively. With the addition of the normalizing factors this induction functor takes unitary representations to unitary representations. One other variation...

openPages displaying short descriptions of redirect targets Stone functor – Functor in category theory Profinite group – Topological group that is in...

from the category of representations of it together with the forgetful functor to the category of vector spaces. The Grothendieck ring of the category...

rings and articulating higher algebraic K-theory in the language of Mackey functors. His work on equivariant higher algebraic K-theory and its generalisations...

"Mackey machine" or "Mackey normal subgroup analysis". From the point of view of category theory, restriction is an instance of a forgetful functor. This...

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...

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...

universal quantifiers can be characterized as special cases of adjoint functors. Back in Zürich for 1968 and 1969 he proposed elementary (first-order)...

India Education Harvard University (BA, PhD) Known for Stone duality Stone functor Stone space Stone's theorem on one-parameter unitary groups Stone's representation...

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...

be viewed as particular kinds of categories, and the representations as functors from the object category to the category of vector spaces. This description...

such that π {\displaystyle \pi } is injective as a function. fiber functor fiber functor. Frobenius reciprocity The Frobenius reciprocity states that for...

in terms of categories of quasicoherent sheaves and flat localization functors. There is also another interesting approach via localization theory, due...

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...