We introduce the notion of integrality Grothendieck categories as a simultaneous generalization primeness noncommutative noetherian rings and locally schemes. Two different spaces associated to category yield respective definitions integrality, we prove equivalence these using Grothendieck-categorical version Gabriel's correspondence, which originally related indecomposable injective modules pr...

Extriangulated categories were introduced by Nakaoka and Palu to give a unification of properties in exact triangulated categories. We consider this article the Grothendieck group K0(C) an extriangulated category C. show that locally finite C always has almost split extensions case relations are generated Auslander-Rieten E-triangles. partial converse result when restricting with cluster tiltin...

Motivated by Wakimoto free field realisations, the bosonic ghost system of central charge c= 2 is studied using a recently proposed formalism for logarithmic conformal field theories. This formalism addresses the modular properties of the theory with the aim being to determine the (Grothendieck) fusion coefficients from a variant of the Verlinde formula. The key insight, in the case of bosonic ...