On g-finiteness in the category of projective presentations

2024/06/06 by Monica Garcia, Garcia, Monica · 1 citation
Computer Science · Decision Sciences · Mathematics · #16E35 #16G10 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2406.04134

openalex publication_date 2024/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide new equivalent conditions for an algebra Λ to be g-finite, analogous to those established by L. Demonet, O. Iyama, and G. Jasso, but within the category of projective presentations K^[-1,0](proj Λ). We show that an algebra has finitely many isomorphism classes of basic 2-term silting objects if and only if all cotorsion pairs in K^[-1,0](proj Λ) are complete. Furthermore, we establish that this criterion is also equivalent to all thick subcategories in K^[-1,0](proj Λ) having enough injective and projective objects.

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