Related papers: Half exact functors associated with cotorsion pair…
Firstly we provide a technique to move torsion pairs in abelian categories via adjoint functors and in particular through Giraud subcategories. We apply this point in order to develop a correspondence between Giraud subcategories of an…
Let $C$ be an additive category with cokernels and let Mod($C$) be the category of additive functors from $C^{op}$ to the category Ab of abelian groups. Let mod($C$) be the full subcategory of Mod($C$) consisting of coherent functors. In…
We show a cotorsion pair cogenerated by a class is complete under suitable conditions in an arbitrary exact category using the generalized small object argument given by Chorny. This recovers Saor\'in and \v{S}\v{t}ov\'{i}\v{c}ek's…
Given a right exact functor from an abelian category into another abelian category, there is an associated abelian category called the comma category of the functor. In this paper, we characterize when left Frobenius pairs (resp. strong…
We study full exact functors between triangulated categories. With some hypotheses on the source category we prove that it admits an orthogonal decomposition into two pieces such that the functor restricted to one of them is zero while the…
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…
We construct Nakayama functors on proper abelian subcategories of triangulated categories with a Serre functor using approximation theory. This, in turn, allows for the construction of Auslander-Reiten translates. As a result, we prove that…
We develop a homotopy theory for additive categories endowed with endofunctors, analogous to the concept of a model structure. We use it to construct the homotopy theory of a Hovey triple (which consists of two compatible complete cotorsion…
Relative theories(=closed subfunctors) are considered in exact, triangulated and extriangulated categories by Dr\"{a}xler-Reiten-Smal{\o}-Solberg-Keller, Beligiannis and Herschend-Liu-Nakaoka, respectively. We give a construction method of…
The purpose of this short and elementary note is to identify some classes of exact categories introduced in L. Previdi's thesis. Among other things we show: (1) An exact category is partially abelian exact if and only if it is abelian. (2)…
In this paper, we consider a kind of ideal quotient of an extriangulated category such that the ideal is the kernel of a functor from this extriangulated category to an abelian category. We study a condition when the functor is dense and…
We construct a functor from the category of graphs to the category of groups which is faithful and "almost" full, in the sense that it induces bijections of the Hom sets up to trivial homomorphisms and conjugation in the category of groups.…
We introduce a notion of exact quasicategory, and we prove an analogue of Amnon Neeman's Theorem of the Heart for Waldhausen K-theory.
In this paper, we first construct some complete cotorson pairs on the category $\mathbb{C}_N(\mathcal{G})$ of unbounded $N$-complexes of Grothendieck category $\mathcal{G}$, from two given cotorsion pairs in $\mathcal{G}$. Next as an…
We study a weight-exact localization pi of a well generated triangulated category C along with the embedding of the hearts of adjacent t-structures coming from the functor right adjoint to pi. We prove that the functors relating the…
If $\mathcal{M}$ is a finite abelian category and $\mathbf{T}$ is a linear right exact monad on $\mathcal{M}$, then the category $\mathbf{T}\mbox{-mod}$ of $\mathbf{T}$-modules is a finite abelian category. We give an explicit formula of…
Nakaoka and Palu introduced the notion of extriangulated categories by extracting the similarities between exact categories and triangulated categories. In this paper, we study cotorsion pairs in a Frobenius extriangulated category $\C$.…
We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…
We define torsion pairs for quasi-abelian categories and give several characterisations. We show that many of the torsion theoretic concepts translate from abelian categories to quasi-abelian categories. As an application, we generalise the…
We show that Quillen's small object argument works for exact categories under very mild conditions. This has immediate applications to cotorsion pairs and their relation to the existence of certain triangulated adjoint functors and model…