RUS  ENG
Full version
JOURNALS // Fundamentalnaya i Prikladnaya Matematika // Archive

Fundam. Prikl. Mat., 2001 Volume 7, Issue 4, Pages 983–992 (Mi fpm606)

Grothendieck categories as quotient categories of $(R\mathrm{\text{-}mod},\mathrm{Ab})$

G. A. Garkusha, A. I. Generalov

Saint-Petersburg State University

Abstract: A Grothendieck category can be presented as a quotient category of the category $(R\mathrm{\text{-}mod},\mathrm{Ab})$ of generalized modules. In turn, this fact is deduced from the following theorem: if $\mathcal C$ is a Grothendieck category and there exists a finitely generated projective object $P\in\mathcal C$, then the quotient category $\mathcal C/\mathcal S^P$, $\mathcal S^P=\{C\in\mathcal C \mid{}_C(P,C)=0\}$ is equivalent to the module category $\mathrm{Mod\text{-}}R$, $R={}_C(P,P)$.

UDC: 512.66

Received: 01.09.1998



Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024