On splitting of morphisms induced by unit map of adjoint functors
Algebraic Geometry
2024-05-13 v1 Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.2405.06610,
title = {On splitting of morphisms induced by unit map of adjoint functors},
author = {Souvik Dey},
journal= {arXiv preprint arXiv:2405.06610},
year = {2024}
}