Zobrazeno 1 - 10
of 783
pro vyhledávání: '"Ivanov, A. O."'
Autor:
Ivanov, Sergei O., Xu, Xiaomeng
We study the concepts of the $\ell_p$-Vietoris-Rips simplicial set and the $\ell_p$-Vietoris-Rips complex of a metric space, where $1\leq p \leq \infty.$ This theory unifies two established theories: for $p=\infty,$ this is the classical theory of Vi
Externí odkaz:
http://arxiv.org/abs/2411.01857
Autor:
Fu, Xin, Ivanov, Sergei O.
For a digraph $G$ without multisquares and a field $\mathbb{F}$, we construct a basis of the vector space of path $n$-chains $\Omega_n(G;\mathbb{F})$ for $n\geq 0$, generalising the basis of $\Omega_3(G;\mathbb{F})$ constructed by Grigory'an. For a f
Externí odkaz:
http://arxiv.org/abs/2407.17001
Autor:
Ivanov, Sergei O., Mukoseev, Lev
The article is devoted to the study of diagonal digraphs, i.e. digraphs whose magnitude homology is concentrated on the diagonal. For a digraph $G$ and $\ell\geq 2,$ we describe a condition, denoted by $(\mathcal{V}_\ell)$, equivalent to vanishing of
Externí odkaz:
http://arxiv.org/abs/2405.04748
In this paper, we study operations on functors in the category of abelian groups simplar to the derivation in the sense of Dold-Puppe. They are defined as derived limits of a functor applied to the relation subgroup over a category of free presentati
Externí odkaz:
http://arxiv.org/abs/2405.03175
Autor:
Asao, Yasuhiko, Ivanov, Sergei O.
We prove that the magnitude (co)homology of an enriched category can, under some technical assumptions, be described in terms of derived functors between certain abelian categories. We show how this statement is specified for the cases of quasimetric
Externí odkaz:
http://arxiv.org/abs/2402.14466
Autor:
Ivanov, Sergei O.
For a real $r\geq 0,$ we consider the notion of $r$-homotopy equivalence in the category quasimetric spaces, which includes metric spaces and directed graphs. We show that for a finite quasimetric space $X$ there is a unique (up to isometry) $r$-homo
Externí odkaz:
http://arxiv.org/abs/2312.11878
Autor:
Carelli, Mishel, Ivanov, Sergei O.
We give a necessary and sufficient condition for an inverse sequence $S_0 \leftarrow S_1 \leftarrow \dots$ indexed by natural numbers to have ${\rm lim}^1S=0$. This condition can be treated as a transfinite version of the Mittag-Leffler condition. We
Externí odkaz:
http://arxiv.org/abs/2310.02716
We consider several types of non-existence theorems for functors. For example, there are no nontrivial functors from the category of groups (or the category of pointed sets, or vector spaces) to any small category. Another type of questions that we c
Externí odkaz:
http://arxiv.org/abs/2306.04432
We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a "bridge" between GLMY-theory and group homology theory, which helps to reduce path homology calculations to gro
Externí odkaz:
http://arxiv.org/abs/2305.15683
We consider the terminal monad among those preserving the objects of a subcategory, and in particular preserving the image of a monad. Several common monads are shown to be uniquely characterized by the property of being terminal objects in the categ
Externí odkaz:
http://arxiv.org/abs/2302.14474