Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Janelidze, Zurab"'
In this paper, we revisit the 1979 work of Isbell on subfactors of groups and their projections, which he uses to establish a stronger formulation of the butterfly lemma and its consequence, the refinement theorem for subnormal series of subgroups. W
Externí odkaz:
http://arxiv.org/abs/2408.05731
In point-free topology, one abstracts the poset of open subsets of a topological space, by replacing it with a frame (a complete lattice, where meet distributes over arbitrary join). In this paper we propose a similar abstraction of the posets of con
Externí odkaz:
http://arxiv.org/abs/2406.16923
Autor:
Janelidze, Zurab
In this paper we construct a wide class of examples of \emph{pretorsion theories} in the sense of A. Facchini, C. Finocchiaro, and M. Gran. Given a category $\mathbb{C}$ with a terminal object $1$ and a category $\mathbb{D}$ with an initial object $0
Externí odkaz:
http://arxiv.org/abs/2311.02666
A noetherian form is an abstract self-dual framework suitable for establishing homomorphism theorems (such as the isomorphism theorems and homological diagram lemmas) for non-abelian, as well as abelian, group-like structures. It can be seen as a uni
Externí odkaz:
http://arxiv.org/abs/2304.03814
Through abelian categories, homological lemmas for modules admit a self-dual treatment, where half of the proof of a lemma is sufficient to prove the full lemma. As remarked in the prequel of the present paper (`Duality in Non-Abelian Algebra IV'), t
Externí odkaz:
http://arxiv.org/abs/2303.11769
Publikováno v:
Theory and Applications of Categories, Vol. 38, 2022, No. 19, pp 737-790
This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the paper giv
Externí odkaz:
http://arxiv.org/abs/2010.16226
In this paper we study maximal chains in certain lattices constructed from powers of chains by iterated lax colimits in the $2$-category of posets. Such a study is motivated by the fact that in lower dimensions, we get some familiar combinatorial obj
Externí odkaz:
http://arxiv.org/abs/2010.01623
A Dedekind-style axiomatization and the corresponding universal property of an ordinal number system
Autor:
Janelidze, Zurab, van der Berg, Ineke
In this paper, we give an axiomatization of the ordinal number system, in the style of Dedekind's axiomatization of the natural number system. The latter is based on a structure $(N,0,s)$ consisting of a set $N$, a distinguished element $0\in N$ and
Externí odkaz:
http://arxiv.org/abs/2006.12688
In this paper we formulate and prove a general theorem of stability of exactness properties under the pro-completion, which unifies several such theorems in the literature and gives many more. The theorem depends on a formal approach to exactness pro
Externí odkaz:
http://arxiv.org/abs/2002.02204
Autor:
Goswami, Amartya, Janelidze, Zurab
Publikováno v:
Advances in Mathematics 349, 2019, 781-812
Abelian categories provide a self-dual axiomatic context for establishing homomorphism theorems (such as the isomorphism theorems and homological diagram lemmas) for abelian groups, and more generally, modules. In this paper we describe a self-dual c
Externí odkaz:
http://arxiv.org/abs/1704.01863