arXiv subjects

Payam Bahiraei

Publications and source records attributed to Payam Bahiraei.

3 recordsLinked to original sources

arXiv2024

Model structures on the category of complexes of quiver representations

In this paper, we study the category $C(Rep(\mathcal{Q}, \mathcal{A}))$ of complexes of representations of quiver $\mathcal{Q}$ with values in an abelian category $\mathcal{A}$. We develop a method for constructing some model structures on $C(Rep(\mathcal{Q}, \mathcal{A}))$ based on componentwise notion. Moreover, we also show that these model structures are monoidal. As an application of these model structures, we introduce some descriptions of the derived category of complexes of representations of $\mathcal{Q}$ in $\Mod R$.

math.RT↗

arXiv2019

Cotorsion pairs and adjoint functors in the homotopy category of $N$-complexes

In this paper, we first construct some complete cotorson pairs on the category $\mathbb{C}_N(\mathcal{G})$ of unbounded $N$-complexes of Grothendieck category $\mathcal{G}$, from two given cotorsion pairs in $\mathcal{G}$. Next as an application, we focus on particular homotopy categories and the existence of adjoint functors between them. These are an $N$-complex version of the results were shown by Neeman in the category of ordinary complexes.

math.RT↗

arXiv2015

Homotopy category of N-complexes of projective modules

In this paper, we show that the homotopy category of N-complexes of projective R-modules is triangle equivalent to the homotopy category of projective T_{N-1}(R)- modules where T_{N-1}(R) is the ring of triangular matrices of order N-1 with entries in R. We also define the notions of N-singularity category and N-totally acyclic complexes. We show that the category of N-totally acyclic complexes of finitely generated projective R-modules embeds in the N-singularity category, which is a result analogous to the case of ordinary chain complexes.

math.RT↗