Characterization of triangular matrix categories via recollements

In this paper, we study triangular matrix categories by using the theory of recollements of abelian categories. Given a triangular matrix category, we construct two canonical recollements. We show that if certain functors of these recollements are exact, then the category appearing in the middle term is actually a category of modules over a triangular matrix category. This result is a generalization of one given by Li (Commun Algebra 46(2):615–628, 2017. https://doi.org/10.1080/00927872.2017.1327051 ). Finally, we show that if Mod(C) Mod ( C ) admits a nontrivial torsion pair by abelian categories, then C C is equivalent to a triangular matrix category.