A note on strong protomodularity, actions and quotients

A note on abelian quotient categories

Let C be a triangulated category with a Serre functor S and X a non-zero contravariantly finite rigid subcategory of C. Then X is cluster tilting if and only if the quotient category C/X is abelian and S(X)=X[2]. As an application, this result generalizes work by Beligiannis.

Recollement of additive quotient categories

In this note, we define a recollement of additive categories, and prove that such a recollement can induce a recollement of their quotient categories. As an application, we get a recollement of quotient triangulated categories induced by mutation pairs.

关于阿贝尔包络的一个注记

A note on abelian envelopes

该研究通过建立Rump商范畴与Bodzenta-Bondal阿贝尔包络这两种泛阿贝尔范畴概念的联系，回答了后者提出的部分基本问题，弥补了正合范畴相关泛阿贝尔范畴概念间的差距。

阿贝尔商与三角商

Abelian versus triangulated quotients

本文证明了三角范畴的局部化可诱导阿贝尔范畴的局部化，并由此构造了仅在更大格罗滕迪克宇宙中存在的阿贝尔商范畴的例子，同时将结果推广到任意范畴的阿贝尔包。

A note on triangulated monads and categories of module spectra

Consider a monad on an idempotent complete triangulated category with the property that its Eilenberg-Moore category of modules inherits a triangulation. We show that any other triangulated adjunction realizing this monad is 'essentially monadic', i.e. becomes monadic after performing the two evident necessary operations of taking the Verdier quotient by the kernel of the right adjoint and idempotent completion. In this sense, the monad itself is 'intrinsically monadic'. It follows that for any highly structured ring spectrum, its category of homotopy (a.k.a. naive) modules is triangulated if …