Related papers: Two results of $n$-exangulated categories
Products in double categories, as found in cartesian double categories, are an elegant concept with numerous applications, yet also have a few puzzling aspects. In this paper, we revisit double-categorical products from an unbiased…
This is an informal (and mostly conjectural) discussion of some aspects of Fukaya categories. We start by looking at exact symplectic manifolds which are obtained from a closed Calabi-Yau by removing a hyperplane section. We look at the…
In this paper, let $(\mathcal{A},\mathcal{B},\mathcal{C})$ be a recollement of extriangulated categories. We introduce the global dimension and extension dimension of extriangulated categories, and give some upper bounds of global…
We study questions motivated by results in the classical theory of dynamical systems in the context of triangulated and A-infinity categories. First, entropy is defined for exact endofunctors and computed in a variety of examples. In…
We define novel fully combinatorial models of higher categories. Our definitions are based on a connection of higher categories to "directed spaces". Directed spaces are locally modelled on manifold diagrams, which are stratifications of…
We propose a generalization of Quillen's exact category -- arithmetic exact category and we discuss conditions on such categories under which one can establish the notion of Harder-Narasimhan filtrations and Harder-Narsimhan polygons.…
This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories…
Associated with some finite dimensional algebras of global dimension at most 2, a generalized cluster category was introduced in \cite{Ami3}, which was shown to be triangulated and 2-Calabi-Yau when it is $\Hom$-finite. By definition, the…
Bondal-Kapranov's notion of enhanced triangulated categories behaves well in the framework of localization theory, in the sense that the Verdier quotient of triangulated categories can be lifted to the Drinfeld dg quotient of…
Braided-enriched monoidal categories were introduced in work of Morrison-Penneys, where they were characterized using braided central functors. Recent work of Kong-Yuan-Zhang-Zheng and Dell extended this characterization to an equivalence…
We generalise to a group homomorphism $\tau$ the $\chi$-graded categories of S\"{o}zer and Virelizier. These are categories in which both morphisms and objects have compatible degrees. We give a 'half-enriched' Yoneda lemma, a structure…
Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…
We give a characterisation of the extriangulated categories which admit the structure of a triangulated category. We show that these are the extriangulated categories where for every object $X$ in the extriangulated category, the morphism…
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory.…
In this paper we first give a simplicial approach to the definition of a non strict $n$-category that we call an $n$-nerve following the idea that a category could be interpreted as a simplicial set, and we prove that our construction…
We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.
We introduce \emph{flagged $(\infty,n)$-categories} and prove that they are equivalent to Segal sheaves on Joyal's category ${\mathbf\Theta}_n$. As such, flagged $(\infty,n)$-categories provide a model-independent formulation of Segal…
One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt the machinery of globular operads [4] to…
We construct an "almost involution" assigning a new DG-category to a given one, and use this construction to recover, say, the abelian category of graded modules over the graded ring $R^*$ from the DG-category of DG-modules over a DG-ring…
We introduce a notion of fine Tannakian infinity-categories and prove Tannakian characterization results for symmetric monoidal stable infinity-categories over a field of characteristic zero. It connects derived quotient stacks with…