Functorially finite subcategories in module categories over Artin algebras have been introduced by Auslander and Smalø [2] to provide a convenient setting for existence of relative Auslander-Reiten sequences in subcategories. Given a functorially finite subcategory, it is generally not well understood how to compute approximations, and the end terms of relative Auslander-Reiten sequences. In th...

We study admissible subcategories of derived categories coherent sheaves on del Pezzo surfaces and rational elliptic surfaces. Using a relation between anticanonical divisors we prove the following results. First, classify all projective plane by showing that each is generated subcollection full exceptional collection. Second, show do not contain any phantom subcategories. This provides first e...

Let $A$ be a right coherent ring and $\mathcal{X}$ contravariantly finite subcategory of ${\rm{mod}}\mbox{-}A$ containing projectives. In this paper, we construct recollement abelian categories $({\rm{mod}}_{0}\mbox{-}\mathcal{X}, {\rm{mod}}\mbox{-}\mathcal{X}, {\rm{mod}}\mbox{-}A)$, where ${\rm{mod}}_{0}\mbox{-}\mathcal{X}$ is full ${\rm{mod}}\mbox{-}\mathcal{X}$ consisting all functors vanish...

Stimuli that capture the central tendency of presented exemplars are often preferred-a phenomenon also known as the classic beauty-in-averageness effect. However, recent studies have shown that this effect can reverse under certain conditions. We propose that a key variable for such ugliness-in-averageness effects is the category structure of the presented exemplars. When exemplars cluster into...