  In an arbitrary Grothendieck category, we find necessary and sufficient
conditions for the class of $\text{FP}_n$-injective objects to be a torsion
class. By doing so, we propose a notion of $n$-hereditary categories. We also
define and study the class of $\text{FP}_n$-flat objects in Grothendieck
categories with a generating set of small projective objects, and provide
several equivalent conditions for this class to be torsion-free. In the end, we
present several applications and examples of $n$-hereditary categories in the
contexts modules over a ring, chain complexes of modules and categories of
additive functors from an additive category to the category of abelian groups.
Concerning the latter setting, we find a characterization of when these functor
categories are $n$-hereditary in terms of the domain additive category.
