Comparison of the Definitions of Abelian 2-categories
نویسنده
چکیده
In the efforts to define a 2-categorical analog of an abelian category, two (or three) notions of “abelian 2-categories” are defined in [4] and [2]. One is the relatively exact 2-category defined in [4], and the other(s) is the (2-)abelian Gpd-category defined by Dupont [2]. We compare these notions, using the arguments in [4] and [2]. Since they proceed independently in their own way, in different settings and terminologies, it will be worth while to collect and unify them. In this paper, by comparing their definitions and arguments, we show the relationship among these classes of 2-categories.
منابع مشابه
On categories of merotopic, nearness, and filter algebras
We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...
متن کاملTORSION CLASSES AND t-STRUCTURES IN HIGHER HOMOLOGICAL ALGEBRA
Higher homological algebra was introduced by Iyama. It is also known as n-homological algebra where n > 2 is a fixed integer, and it deals with n-cluster tilting subcategories of abelian categories. All short exact sequences in such a subcategory are split, but it has nice exact sequences with n + 2 objects. This was recently formalised by Jasso in his theory of n-abelian categories. There is a...
متن کاملGorenstein projective objects in Abelian categories
Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...
متن کاملThe non-abelian tensor product of normal crossed submodules of groups
In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...
متن کاملThe Structure of Plant Population of Forested Rangeland in Different Legal Definitions (Case Study: Sabzkouh Region, Chaharmahal & Bakhtiari Province, Iran)
There is less published research on ecosystems of forested rangeland in Iran. This research was conducted to investigate the forested rangeland area based on legal definition via comparison of indices species richness, diversity, and morphology of the trees and shrubs in Sabzkouh watershed, Chaharmahal Bakhtiari province, Iran. Quantitative characteristics of trees and shrubs were measured by 5...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009