相关论文: Abelian envelopes of exact categories and highest …

We study aisles in the derived category of a hereditary abelian category. Given an aisle, we associate a sequence of subcategories of the abelian category by considering the different homologies of the aisle. We then obtain a sequence,…

Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…

We introduce a relative tilting theory in abelian categories and show that this work offers a unified framework of different previous notions of tilting, ranging from Auslander-Solberg relative tilting modules on Artin algebras to…

It is a well established fact that the notions of quasi-abelian categories and tilting torsion pairs are equivalent. This equivalence fits in a wider picture including tilting pairs of $t$-structures. Firstly, we extend this picture into a…

We define model structures on exact categories which we call exact model structures. We look at the relationship between these model structures and cotorsion pairs on the exact category. In particular, when the underlying category is weakly…

Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category $\mathcal O$. An analogue of the PBW theorem will be shown to hold for…

Integral categories form a sub-class of pre-abelian categories whose systematic study was initiated by Rump in 2001. In the first part of this article we determine whether several categories of topological and bornological vector spaces are…

We introduce and investigate (dual) relative split objects with respect to a fully invariant short exact sequence in abelian categories. We compare them with (dual) relative Rickart objects, and we study their behaviour with respect to…

For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection we classify thick…

For an abelian tensor category a stack is constructed. As an application we show that our construction can be used to recover a quasi-compact separated scheme from the category of its quasi-coherent sheaves. In another application, we show…

We introduce the notion of an exact dg category, which is a simultaneous generalization of the notions of exact category in the sense of Quillen and of pretriangulated dg category in the sense of Bondal--Kapranov. It is also a differential…

We continue our study of relatively divisible and relatively flat objects in exact categories in the sense of Quillen with several applications to exact structures on finitely accessible additive categories and module categories. We derive…

For a locally presentable abelian category $\mathsf B$ with a projective generator, we construct the projective derived and contraderived model structures on the category of complexes, proving in particular the existence of enough homotopy…

We show that a direct limit of projective contramodules (over a right linear topological ring) is projective if it has a projective cover. A similar result is obtained for $\infty$-strictly flat contramodules of projective dimension not…

We construct a category $\OrdFor$ as an arboreal extension of $\Delta_{\mathrm{epi}}\subseteq\Delta$, whose morphisms are ordered forests composed by grafting. We define a full functor $\pi\colon \OrdFor\to\Delta_{\mathrm{epi}}^{op}$…

We show that, with some technical conditions, an abelian category can be embedded into the category of bimodules over a ring. The case of semisimple rigid monoidal categories is studied in more detail.

We show that Klemenc's stable envelope of exact $\infty$-categories induces an equivalence between stable $\infty$-categories with a bounded heart structure and weakly idempotent complete exact $\infty$-categories. Moreover, we generalise…

We introduce and study relatively divisible and relatively flat objects in exact categories in the sense of Quillen. For every relative cotorsion pair $(\mathcal{A},\mathcal{B})$ in an exact category $\mathcal{C}$, $\mathcal{A}$ coincides…

Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In…

Sieg and Wegner showed that the stable exact sequences define a maximal exact structure (in the sense of Quillen) in any pre-abelian category. We generalize this result for weakly idempotent complete additive categories.