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.
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