Gorenstein flat representations of left rooted quivers

[摘要] We study Gorenstein flat objects in the category Rep(Q, R) of representations of a left rooted quiver Q with values in Mod(R), the category of all left R-modules, where R is an arbitrary associative ring. We show that a representation X in Rep(Q, R) is Gorenstein flat if and only if for each vertex i the canonical homomorphism phi(X)(i) : circle plus X-a:j -> i(j) -> X(i) is injective, and the left R-modules X(i) and Coker phi(X)(i) are Gorenstein flat. As an application, we obtain a Gorenstein flat model structure on Rep(Q, R) in which we give explicit descriptions of the subcategories of trivial, cofibrant and fibrant objects. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-15

[关键词] Left rooted quiver;Gorenstein flat representation;Model structure