Differential graded triangular matrix categories

This paper focuses on defining an analog of differential-graded triangular matrix algebra in the context of differential-graded categories. Given two dg-categories \(\mathcal{U}\) and \(\mathcal{T}\) and \(M \in \text{DgMod}(\mathcal{U} \otimes \mathcal{T}^{\text{op}})\), we construct the differenti...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: M Lizbeth Shaid Sandoval Miranda, Valente Santiago Vargas, Velasco Páez, Edgar O
Format: Article
Language:English
Subjects:
Categories
Matrices (mathematics)
Matrix algebra
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper focuses on defining an analog of differential-graded triangular matrix algebra in the context of differential-graded categories. Given two dg-categories \(\mathcal{U}\) and \(\mathcal{T}\) and \(M \in \text{DgMod}(\mathcal{U} \otimes \mathcal{T}^{\text{op}})\), we construct the differential graded triangular matrix category \(\Lambda := \left( \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix} \right)\). Our main result is that there is an equivalence of dg-categories between the dg-comma category \((\text{DgMod}(\mathcal{T}),\text{GDgMod}(\mathcal{U}))\) and the category \(\text{DgMod}\left( \left( \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix} \right)\right)\). This result is an extension of a well-known result for Artin algebras (see, for example, [2,III.2].
ISSN:2331-8422