Let $\mathcal {A} $ be a locally bounded $ k $-category and $ G $ a torsion-free group of $ k
$-linear automorphisms of $\mathcal {A} $ acting freely on the objects of $\mathcal {A}, $ and …

We construct two functors from the submodule category of a representation-finite self-
injective algebra Λ to the module category of the stable Auslander algebra of Λ. These …

The theory of morphisms being determined by objects was originally investigated by
Auslander, and can be seen as the culmination part of Auslander-Reiten theory. This theory …

In several familiar subcategories of the category ${\mathbb T} $ of topological spaces and
continuous maps, embeddings are not pushout-stable. But, an interesting feature …

For a nice-enough category $\mathcal {C} $, we construct both the morphism category ${\rm
H}(\mathcal {C}) $ of $\mathcal {C} $ and the category ${\rm mod}\mbox {-}\mathcal {C} $ of …

The center $ Z (\mathcal {A}) $ of an abelian category $\mathcal {A} $ is the endomorphism
ring of the identity functor on that category. A localizing subcategory of a Grothendieck …

Let G be a group of automorphisms of a category C. We give a definition for a functor F: C→
C′ to be a G-covering and three constructions of the orbit category C/G, which generalizes …

We generalize Ringel and Schmidmeier's theory on the Auslander–Reiten translation of the
submodule category 𝒮 2 (A) to the monomorphism category 𝒮 n (A); the category consists of …

For an arbitrary finite dimensional algebra $\Lambda $, we prove that any wide subcategory
of $\mathsf {mod}\Lambda $ satisfying a certain finiteness condition is $\theta $-semistable …

We set up a general theory of weak or homotopy-coherent enrichment in an arbitrary
monoidal∞-category. Our theory of enriched∞-categories has many desirable properties; …