Gorenstein projective objects and recollements of Abelian categories
Peiyu Zhang, Qianqian Shu, Dajun Liu

TL;DR
This paper explores the connections of Gorenstein projective objects in three Abelian categories within a recollement, introducing n-Gorenstein tilting modules and analyzing how resolving subcategories influence global dimensions.
Contribution
It establishes how resolving subcategories relate across three Abelian categories in a recollement and introduces n-Gorenstein tilting modules in this context.
Findings
Resolving subcategories induce and are induced by other resolving subcategories.
The size relationship between the relative global dimensions of the categories.
Introduction of n-Gorenstein tilting modules and Gorenstein syzygy modules.
Abstract
In this paper, we study the relationship of Gorenstein projective objects among three Abelian categories in a recollement. As an application, we introduce the relation of -Gorenstein tilting modules (and Gorenstein syzygy modules) in three Abelian categories. For a recollement of Abelian categories, we show that a resolving subcategory induce two resolving subcategories. On the other hand, we also prove that two resolving subcategories can induce a resolving subcategory. Moreover, we give the size relationship between the relative global dimensions of three Abelian categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Axial and Atropisomeric Chirality Synthesis
