Abstract
Let Λ be an artin algebra and be a quasi-resolving subcategory of
which is of finite type. Let
be the full subcategory of the morphism category
consisting of all monomorphisms
in
such that
also lies in
. In this paper, we state and prove Brauer-Thrall type theorems for
. As applications, we provide necessary and sufficient conditions for the submodule category
to be of finite type, whenever Λ is of finite representation type, as well as, for the lower 2 × 2 triangular matrix algebra
to be of finite CM-type, whenever Λ is of finite CM-type.