Related papers: Localizations of (one-sided) exact categories
Categories of locally ordered spaces are especially well-adapted to the realization of most precubical sets, though their colimits are not so easy to determine (in comparison with colimits in the category of d-spaces for example). We use…
Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. A notion of mutation of subcategories in an extriangulated category is defined in this…
In this paper we study a 2-dimensional version of Quillen's homotopy category construction. Given a category $\mathscr{A}$ and a class of morphisms $\Sigma \subset \mathscr{A}$ containing the identities, we construct a 2-category…
We survey the basics of homological algebra in exact categories in the sense of Quillen. All diagram lemmas are proved directly from the axioms, notably the five lemma, the 3 x 3-lemma and the snake lemma. We briefly discuss exact functors,…
The notion of $n$-exangulated categories was introduced by Herschend-Liu-Nakaoka, which is a simultaneous generalization of $n$-exact categories in the sense of Jasso and $(n+2)$-angulated categories in the sense of Geiss-Kelier-Oppermann.…
We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently…
We give a sufficient condition for a Verdier quotient $\ct/\cs$ of a triangulated category $\ct$ by a thick subcategory $\cs$ to be realized inside of $\ct$ as an ideal quotient. As applications, we deduce three significant results by…
We show how to obtain recollements of triangulated categories using the theory of exact model structures. After noting how the theory relates to well-known notions in the simplest case of Frobenius categories, we apply these ideas to…
We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category…
Let (X, O_X) be a noetherian formal scheme and consider D_qct(X) its derived category of sheaves with quasi-coherent torsion homology. We show that there is a bijection between the set of rigid (i.e. \tensor-ideals) localizing subcategories…
We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…
It is shown that any localisation of triangulated categories induces (up to an equivalence) a localisation of abelian categories when one passes to their abelianisations. From this one obtains for any enlargement of Grothendieck universes…
In this paper, we first provide an explicit procedure to glue together hereditary exact model structures for the recollement of exact categories. To that end, we use the notion of cotorsion pairs and we investigate the gluing of complete…
Let $n$ be an integer greater or equal than $3$. We give a simultaneous generalization of $(n-2)$-exact categories and $n$-angulated categories, and we call it one-sided $n$-suspended categories. One-sided $n$-angulated categories are also…
We prove that some subquotient categories of one-sided triangulated categories are abelian. This unifies a result by Iyama-Yoshino in the case of triangulated categories and a result by Demonet-Liu in the case of exact categories.
We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly: Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss standard results for tilting subcategories:…
Our first aim is to provide an analog of the Gabriel-Quillen embedding theorem for $n$-exact categories. Also we give an example of an $n$-exact category that is not an $n$-cluster tilting subcategory, and we suggest two possible ways for…
Our aim is to give a fairly complete account on the construction of compatible model structures on exact categories and symmetric monoidal exact categories, in some cases generalizing previously known results. We describe the close…
Weakly approximable triangulated categories, introduced by Neeman, provide a powerful framework for studying localization phenomena in triangulated categories. In this paper, we establish new localization theorems showing that, under mild…
We develop the K-theory of sets with an action of a pointed monoid (or monoid scheme), analogous to the $K$-theory of modules over a ring (or scheme). In order to form localization sequences, we construct the quotient category of a nice…