We study localizing and colocalizing subcategories of a comodule category of a coalgebra C over a field, using the correspondence between localizing subcategories and equivalence classes of idempotent elements in the dual algebra C∗. In this framework, we give a useful description of the localization functor by means of the Morita–Takeuchi context defined by the quasi-finite injective cogenerat...

Let R be a commutative Noetherian Henselian local ring. Denote by modR the category of finitely generated R-modules, and by G the full subcategory of modR consisting of all G-projective R-modules. In this paper, we consider when a given R-module has a right G-approximation. For this, we study the full subcategory rapG of modR consisting of all R-modules that admit right G-approximations. We inv...

Abstract Let $\mathcal{M}$ be a small $n$-abelian category. We show that the category of finitely presented functors ${\operatorname{mod}}$-$\mathcal{M}$ modulo subcategory effaceable ${\operatorname{mod}}_0$-$\mathcal{M}$ has an $n$-cluster tilting subcategory, which is equivalent to $\mathcal{M}$. This gives higher-dimensional version Auslander’s formula.

There are two main approaches to obtaining \topological" cartesian-closed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed | for example, the category of sequential spaces. Under the other, one generalises the notion of space | for example, to Scott's notion of equilogical space. In this paper we show that the two appr...

Given a poset P , the set Γ(P ) of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Posd (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P ) ∼= Γ(Q) implies P ∼= Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Posd is not....

For an Artinian (n− 1)-Auslander algebra Λ with global dimension n(≥ 2), we show that if Λ admits a trivial maximal (n − 1)-orthogonal subcategory of modΛ, then Λ is a Nakayama algebra. Further, for a finite-dimensional algebra Λ over an algebraically closed field K, we show that Λ is a basic and connected (n−1)-Auslander algebra Λ with global dimension n(≥ 2) admitting a trivial maximal (n− 1)...

There are various doctrines wherein theories are small categories and the models of a theory constitute a full subcategory of the category of functors from the theory to sets. We define the notion of bimodel at the nondoctrinaire level where those specified subcategories are arbitrary; as a first application we look for a classification of the equivalences between categories of models. We obtai...

Given a poset P , the set, Γ(P), of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Pos d (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P) ∼ = Γ(Q) implies P ∼ = Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Pos d is ...

In this paper, we study fusion categories which contain a proper subcategory with maximal rank. They can be viewed as generalizations of near-group categories. We first prove that they admit spherical structure. then classify those are non-degenerate or symmetric. Finally, such rank 4.