Gorenstein Objects in Extriangulated Categories
Zhenggang He

TL;DR
This paper explores Gorenstein objects within extriangulated categories, defining new types of projective resolutions and characterizing their properties to advance understanding of relative Gorenstein theory.
Contribution
It introduces the notion of $\xi$-$ ext{G}$projective resolutions and characterizes $\xi$-$n$-strongly $ ext{G}$projective objects, expanding the framework of Gorenstein objects in extriangulated categories.
Findings
Established equivalences between different types of $\xi$-projective resolutions.
Defined and characterized $\xi$-$n$-strongly $ ext{G}$projective objects.
Provided properties and relations of these objects within the category.
Abstract
This paper mainly studies the relative Gorenstein objects in the extriangulated category with a proper class and the related properties of these objects. In the first part, we define the notion of the -projective resolution, and study the relation between -projective resolution and -projective resolution for any object in , i.e. has a -exact -projective resolution if and only if has a -exact -projective resolution. In the second part, we define a particular -Gorenstein projective object in which called --strongly projective object. On this basis, we study the relation between --strongly projective object and…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons
