From simplicial homotopy to crossed module homotopy in modified categories of interest
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
From simplicial homotopy to crossed module homotopy in modified categories of interest
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Georgian Mathematical Journal
ISSN
1072-947X
e-ISSN
1572-9176
Volume of the periodical
27
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
16
Pages from-to
541-556
UT code for WoS article
000586530400005
EID of the result in the Scopus database
2-s2.0-85057025469