From simplicial homotopy to crossed module homotopy in modified categories of interest

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00117625" target="_blank" >RIV/00216224:14310/20:00117625 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1515/gmj-2018-0069" target="_blank" >https://doi.org/10.1515/gmj-2018-0069</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/gmj-2018-0069" target="_blank" >10.1515/gmj-2018-0069</a>

Jazyk výsledku

angličtina

Název v původním jazyce

From simplicial homotopy to crossed module homotopy in modified categories of interest

Popis výsledku v původním jazyce

We address the (pointed) homotopy of crossed module morphisms in modified categories of interest that unify the notions of groups and various algebraic structures. We prove that the homotopy relation gives rise to an equivalence relation as well as to a groupoid structure with no restriction on either domain or co-domain of the corresponding crossed module morphisms. Furthermore, we also consider particular cases such as crossed modules in the categories of associative algebras, Leibniz algebras, Lie algebras and dialgebras of the unified homotopy definition. Finally, as one of the major objectives of this paper, we prove that the functor from simplicial objects to crossed modules in modified categories of interest preserves the homotopy as well as the homotopy equivalence.

Název v anglickém jazyce

From simplicial homotopy to crossed module homotopy in modified categories of interest

Popis výsledku anglicky

We address the (pointed) homotopy of crossed module morphisms in modified categories of interest that unify the notions of groups and various algebraic structures. We prove that the homotopy relation gives rise to an equivalence relation as well as to a groupoid structure with no restriction on either domain or co-domain of the corresponding crossed module morphisms. Furthermore, we also consider particular cases such as crossed modules in the categories of associative algebras, Leibniz algebras, Lie algebras and dialgebras of the unified homotopy definition. Finally, as one of the major objectives of this paper, we prove that the functor from simplicial objects to crossed modules in modified categories of interest preserves the homotopy as well as the homotopy equivalence.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Georgian Mathematical Journal

ISSN

1072-947X

e-ISSN

1572-9176

Svazek periodika

27

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

16

Strana od-do

541-556

Kód UT WoS článku

000586530400005

EID výsledku v databázi Scopus

2-s2.0-85057025469