On splitting of morphisms induced by unit map of adjoint functors

Fuente: arXiv
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Autor principal: Dey, Souvik
Formato: Preprint
Publicado: 2024
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author Dey, Souvik
author_facet Dey, Souvik
contents Given a right adjoint functor between triangulated categories and an object in the target category, we show that the unit map of adjunction on that object is a split monomorphism if and only if the object belongs to the additive closure of (all possible) shifts of an object in the image of the functor. Applications to geometric context related to (derived) splinters and rational singularities are given.
format Preprint
id arxiv_https___arxiv_org_abs_2405_06610
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On splitting of morphisms induced by unit map of adjoint functors
Dey, Souvik
Algebraic Geometry
Commutative Algebra
Given a right adjoint functor between triangulated categories and an object in the target category, we show that the unit map of adjunction on that object is a split monomorphism if and only if the object belongs to the additive closure of (all possible) shifts of an object in the image of the functor. Applications to geometric context related to (derived) splinters and rational singularities are given.
title On splitting of morphisms induced by unit map of adjoint functors
topic Algebraic Geometry
Commutative Algebra
url https://arxiv.org/abs/2405.06610