Idempotent triples and completion

Deleanu, Aristide; Frei, Armin; Hilton, Peter

doi:10.1007/bf01173053

Cited by 13 publications

(5 citation statements)

References 6 publications

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“…If C is a (small) category, the category End(C) of functors C −→ C is a strictly associative and strictly unital monoidal category with respect to composition of functors. Closed idempotents in this category were studied, under the name of idempotent monads, in a number of earlier works, among which we mention [Ad73,DFH74,DFH75]. In this subsection we summarize the basic facts relating idempotent monads to the notions of adjoint functors and reflective subcategories, mostly following [KS06, §4.1] (the term "projector" is used in loc.…”

Section: Semigroupal and Monoidal Functorsmentioning

confidence: 99%

Character sheaves on unipotent groups in positive characteristic: foundations

Boyarchenko

Drinfeld

2013

Sel. Math. New Ser.

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OverviewThese are slides for a talk given by the authors at the conference "Current developments and directions in the Langlands program" held in honor of Robert Langlands at the Northwestern University in May of 2008. The research program outlined in this talk was realized in a series of articles [1]- [4]. The orbit method for unipotent groups in positive characteristic is discussed in [1]. The results on character sheaves discussed in parts I and II of this talk are proved in [3]. The results described in part III are proved in [2] and [4]; the former studies L-packets of irreducible characters and the latter is devoted to the relationship between characters and character sheaves on unipotent groups over finite fields.We will outline a theory that combines some of the essential features of Lusztig's theory and of the orbit method.

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Section: Semigroupal and Monoidal Functorsmentioning

confidence: 99%

Character sheaves on unipotent groups in positive characteristic: foundations

Boyarchenko

Drinfeld

2013

Sel. Math. New Ser.

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“…In [13] they are investigated in the context of localisation and duality (1975). In the same year they were studied in [10,Section 2] where it is shown that their Kleisli categories are isomorphic to the category of fractions (of invertible morphisms). Extending these ideas, idempotent approximations to any monad are the topic of [5].…”

Section: Remarksmentioning

confidence: 98%

Idempotent monads and ⋆-functors

Clark¹,

Wisbauer²

2011

Journal of Pure and Applied Algebra

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a b s t r a c tFor an associative ring R, let P be an R-module with S = End R (P). C. Menini and A. Orsatti posed the question of when the related functor Hom R (P, −) (with left adjoint P ⊗ S −) induces an equivalence between a subcategory of R M closed under factor modules and a subcategory of S M closed under submodules. They observed that this is precisely the case if the unit of the adjunction is an epimorphism and the counit is a monomorphism. A module P inducing these properties is called a -module.The purpose of this paper is to consider the corresponding question for a functor G : B → A between arbitrary categories. We call G a -functor if it has a left adjoint F : A → B such that the unit of the adjunction is an extremal epimorphism and the counit is an extremal monomorphism. In this case (F , G) is an idempotent pair of functors and induces an equivalence between the category A GF of modules for the monad GF and the category B FG of comodules for the comonad FG. Moreover, B FG = Fix(FG) is closed under factor objects in B, A GF = Fix(GF ) is closed under subobjects in A.

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“…Given any extension of groups there exists a spectral sequence { E pq }, with E pq =H ( Q; H M), converging finitely to the graded group associated with H * G , suitably filtered. 4. Localization of nilpotent groups.…”

Section: Propositionmentioning

confidence: 99%

“…1) in N , (f is a P -isomorphism if and only if 0P is an isomorphism.. It now follows (see [4] ) that the P -isomorphisms of N are pre-cisely those morphisms of N which are rendered invertible by the localization functor; we are thus led to the general theory of completions as in [3,4], but we do not take that direction here. Instead, we draw some immediate consequences.…”

Section: P -Isomorphismsmentioning

confidence: 99%

See 1 more Smart Citation

Localization and cohomology of nilpotent groups

Hilton

1973

Math Z

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Cahiers de topologie et géométrie différentielle catégoriques, tome 14, n o 4 (1973), p. 341-369 © Andrée C. Ehresmann et les auteurs, 1973, tous droits réservés. L'accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

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Idempotent triples and completion

Cited by 13 publications

References 6 publications

Character sheaves on unipotent groups in positive characteristic: foundations

Character sheaves on unipotent groups in positive characteristic: foundations

Idempotent monads and ⋆-functors

Localization and cohomology of nilpotent groups

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