A Universal Coefficient Theorem for Categories with Kernels.
A universal construction in Goursat categories
A useful category for mixed Abelian groups.
Abelian groupoids and non-pointed additive categories.
Action groupoid in protomodular categories.
Additive Duality at Cosmall Injectives
Almost abelian categories
Catégories préadditives structurées
Closedness properties of internal relations. IV: Expressing additivity of a category via subtractivity.
Enriched model categories and an application to additive endomorphism spectra.
Étude élémentaire des catégories
Exact couples in a Raïkov semi-abelian category
Functors on locally finitely presented additive categories
-quasi-Frobenius Lie algebras
A Lie version of Turaev’s -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a -quasi-Frobenius Lie algebra for a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra together with a left -module structure which acts on via derivations and for which is -invariant. Geometrically, -quasi-Frobenius Lie algebras are the Lie algebra structures associated to symplectic...
Galois coverings, Morita equivalence and smash extensions of categories over a field.
Graphes sans circuit et bilinéarité
Hall algebras of two equivalent extriangulated categories
For any positive integer , let be a linearly oriented quiver of type with vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories and , where and are the two extriangulated categories corresponding to the representation category of and the morphism category of projective representations of , respectively. As a by-product,...
Idempotent completion of pretriangulated categories
A pretriangulated category is an additive category with left and right triangulations such that these two triangulations are compatible. In this paper, we first show that the idempotent completion of a left triangulated category admits a unique structure of left triangulated category and dually this is true for a right triangulated category. We then prove that the idempotent completion of a pretriangulated category has a natural structure of pretriangulated category. As an application, we show that...
On deformations of pasting diagrams.
On the maximal exact structure of an additive category
We prove that every additive category has a unique maximal exact structure in the sense of Quillen.