A recollement of differential graded categories

TL;DR

This paper establishes a canonical recollement structure for differential graded categories involving subcategories and extends the theory to triangular matrix categories, generalizing previous results.

Contribution

It proves the existence of a canonical recollement for dg-categories with certain subcategories and extends the concept to dg-triangular matrix categories, broadening the theoretical framework.

Findings

Established a canonical recollement for dg-categories with subcategories.

Extended recollement concepts to dg-triangular matrix categories.

Generalized previous results by Chen and Zheng on dg-categories.

Abstract

In this paper, we prove that given a differential graded category C and B a full differential graded subcategory closed under coproducts, there is a canonical recollement of differential graded categories, for which we use enriched categories tools. We continue the study of differential graded triangular matrix categories as initiated in [22]. We show that given a recollement between functor dg-categories we can induce a new recollement between differential graded triangular matrix categories, this is a generalization of a result given by Chen and Zheng in [5, Theorem 4.4].