Abstract 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.
Sandoval-Miranda et al. (Mon,) studied this question.