An axiomatic survey of diagram lemmas for non-abelian group-like structures
Reads0
Chats0
TLDR
In this article, it is shown that the snake lemma and the 3 × 3 lemma are equivalent to each other for all (pointed) algebraic structures, and also in general categories of a special type.About:
This article is published in Journal of Algebra.The article was published on 2012-11-15 and is currently open access. It has received 7 citations till now. The article focuses on the topics: Five lemma & Snake lemma.read more
Citations
More filters
Journal ArticleDOI
On the Form of Subobjects in Semi-Abelian and Regular Protomodular Categories
TL;DR: The conditions which are used to characterize semi-abelian and regular protomodular categories can be stated as self-dual conditions on the bifibration corresponding to the form of subobjects.
Journal ArticleDOI
Duality in non-abelian algebra III. Normal categories and 0-regular varieties
TL;DR: In this article, a self-dual axiomatic approach to normal categories is presented, which uses self-duality on a functor defined using subobjects of objects in the category, and a similar approach can be developed for 0-regular varieties, if we replace subobjects with subsets of algebras containing 0.
Journal ArticleDOI
A Note on the Abelianization Functor
Dominique Bourn,Zurab Janelidze +1 more
TL;DR: In this article, it was shown that the abelianization of a group G can be computed as the cokernel of the diagonal morphism (1G, 1G): G→ G×G×G in the category of groups.
Journal ArticleDOI
The snail lemma in a pointed regular category
Zurab Janelidze,Enrico Vitale +1 more
TL;DR: In this paper, it was shown that under the presence of cokernels of kernels, the validity of the snail lemma is equivalent to subtractivity of the pointed regular category.
Dissertation
Bifibrational duality in non-abelian algebra and the theory of databases
TL;DR: In this article, a self-dual categorical approach to some topics in non-abelian algebra is developed, which is based on replacing the framework of a category with a category equipped with a functor to it.
References
More filters
Book
Categories for the Working Mathematician
TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.
MonographDOI
Handbook of Categorical Algebra
TL;DR: The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen.
Journal ArticleDOI
Semi-abelian categories
TL;DR: Semi-abelian categories as mentioned in this paper allow for a generalized treatment of abelian-group and module theory, and have a finite coproducts and a zero object.
Book
Mal'cev, Protomodular, Homological and Semi-Abelian Categories
Francis Borceux,Dominique Bourn +1 more
TL;DR: In this article, the Yoneda embedding is used to embed points in the fibration of points, which is a set of classes of objects in the Mal'cev categories.
Book
Mal'cev Varieties
TL;DR: Rudiments and notations as mentioned in this paper : Centrality, direct decomposition, central isotopy and cancellation, plain algebras and equational completeness, extensions and obstructions.