On the representaion type of locally bounded categories

Algebras with cycle-finite Galois coverings

“…Recall that, following Drozd [Dro], a finite category R is called tame if, for any dimension d, there exists a finite number [CB2]). An arbitrary locally bounded category R is said to be tame (respectively, of polynomial growth, domestic) if so is every finite full subcategory of R. We refer to [DS2] for results characterizing tame locally bounded categories. It has been proved in [DS1] that if R is a locally bounded category, G a group of automorphisms of R acting freely on the objects of R and R/G is tame, then R is tame.…”

Selfinjective algebras of tubular type

“…Following [10], a finite bounded category R is said to be tame if, for any dimension d, there exists a finite number of [31]). Finally, an arbitrary locally bounded category R is said to be tame (respectively, of polynomial growth) if so is every finite full subcategory of R (see [8]). …”

On the Notion of Derived Tameness

“…This result carries over to arbitrary locally bounded categories. To this end recall that Dowbor and Skowroński have shown that the tame representation type of a locally bounded category is characterized by the fact that every finite full subcategory is of tame representation type [5].…”