Sheaves over infinite posets-Reference-Cited by-同舟云学术

Sheaves over infinite posets

Published:2017-02 Issue:02 Volume:16 Page:1750026
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Asadollahi J.¹²,Bahiraei P.¹,Hafezi R.²,Vahed R.²

Affiliation:

1. Department of Mathematics, University of Isfahan, P. O. Box 81746-73441, Isfahan, Iran

2. School of Mathematics, Institute for Research in Fundamental Science (IPM), P. O. Box 19395-5746, Tehran, Iran

Abstract

In this paper, we study the category of sheaves over an infinite partially ordered set with its natural topological structure. Totally acyclic complexes in this category will be characterized in terms of their stalks. This leads us to describe Gorenstein projective, injective and flat sheaves. As an application, we get an analogue of a formula due to Mitchell, giving an upper bound on the Gorenstein global dimension of such categories. Based on these results, we present situations in which the class of Gorenstein projective sheaves is precovering as well as situations in which the class of Gorenstein injective sheaves is preenveloping.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498817500268

Reference33 articles.

1. On the homotopy categories of projective and injective representations of quivers

2. Cohen–Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras

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