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On a Lift of an Individual Stable Equivalence to a Standard Derived Equivalence for Representation-Finite Self-injective Algebras
We shall show that every stable equivalence (functor) between representation-finite self-injective algebras not of type (D3m,s/3,1) with m≥2, 3∤s lifts to a standard derived equivalence. This implies
A generalization of Gabriel's Galois covering functors and derived equivalences
Let $G$ be a group acting on a category $\mathcal{C}$. We give a definition for a functor $F\colon \mathcal{C} \to \mathcal{C}'$ to be a $G$-covering and three constructions of the orbit category
On Interval Decomposability of 2D Persistence Modules
In persistent homology of filtrations, the indecomposable decompositions provide the persistence diagrams. In multidimensional persistence it is known to be impossible to classify all indecomposable
Gluing derived equivalences together
The Grothendieck construction of a diagram $X$ of categories can be seen as a process to construct a single category $\Gr(X)$ by gluing categories in the diagram together. Here we formulate diagrams
On Approximation of $2$D Persistence Modules by Interval-decomposables
In this work, we propose a new invariant for $2$D persistence modules called the compressed multiplicity and show that it generalizes the notions of the dimension vector and the rank invariant. In
Matrix method for persistence modules on commutative ladders of finite type
The theory of persistence modules on the commutative ladders $$CL_n(\tau )$$CLn(τ) provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence