POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF
COMMUTATIVE ALGEBRAS

J 2016

POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS

AKCA, Ilker; Kadir EMIR a Joao Faria MARTINS

Základní údaje

Originální název

POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS

Autoři

AKCA, Ilker; Kadir EMIR a Joao Faria MARTINS

Vydání

Homology, Homotopy and Applications, SOMERVILLE, Droz, 2016, 1532-0073

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.486

Označené pro přenos do RIV

DOI

https://doi.org/10.4310/HHA.2016.v18.n1.a6

UT WoS

000383324400006

Klíčová slova anglicky

simplicial commutative algebra; crossed module of commutative algebras; 2-crossed module of commutative algebras; quadraticderivation

Štítky

RIV ne

Změněno: 21. 2. 2019 14:41, Kadir Emir, Ph.D.

Anotace

V originále

We address the homotopy theory of 2-crossed modules of commutative algebras, which are equivalent to simplicial commutative algebras with Moore complex of length two. In particular, we construct for maps of 2-crossed modules a homotopy relation, and prove that it yields an equivalence relation in very unrestricted cases (freeness up to order one of the domain 2-crossed module). This latter condition strictly includes the case when the domain is cofibrant. Furthermore, we prove that this notion of homotopy yields a groupoid with objects being the 2-crossed module maps between two fixed 2-crossed modules (with free up to order one domain), the morphisms being the homotopies between 2-crossed module maps.

Citovat

AKCA, Ilker; Kadir EMIR a Joao Faria MARTINS. POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS. Homology, Homotopy and Applications. SOMERVILLE: Droz, 2016, roč. 18, č. 1, s. 99-128. ISSN 1532-0073. Dostupné z: https://doi.org/10.4310/HHA.2016.v18.n1.a6.

@article{1472606,
   author = {Akca, Ilker and Emir, Kadir and Martins, Joao Faria},
   article_location = {SOMERVILLE},
   article_number = {1},
   doi = {https://doi.org/10.4310/HHA.2016.v18.n1.a6},
   keywords = {simplicial commutative algebra; crossed module of commutative algebras; 2-crossed module of commutative algebras; quadraticderivation},
   language = {eng},
   issn = {1532-0073},
   journal = {Homology, Homotopy and Applications},
   title = {POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS},
   url = {http://dx.doi.org/10.4310/HHA.2016.v18.n1.a6},
   volume = {18},
   year = {2016}
}

TY  - JOUR
ID  - 1472606
AU  - Akca, Ilker - Emir, Kadir - Martins, Joao Faria
PY  - 2016
TI  - POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS
JF  - Homology, Homotopy and Applications
VL  - 18
IS  - 1
SP  - 99-128
EP  - 99-128
PB  - Droz
SN  - 15320073
KW  - simplicial commutative algebra
KW  - crossed module of commutative algebras
KW  - 2-crossed module of commutative algebras
KW  - quadraticderivation
UR  - http://dx.doi.org/10.4310/HHA.2016.v18.n1.a6
L2  - http://dx.doi.org/10.4310/HHA.2016.v18.n1.a6
N2  - We address the homotopy theory of 2-crossed modules of commutative algebras, which are equivalent to simplicial commutative algebras with Moore complex of length two. In particular, we construct for maps of 2-crossed modules a homotopy relation, and prove that it yields an equivalence relation in very unrestricted cases (freeness up to order one of the domain 2-crossed module). This latter condition strictly includes the case when the domain is cofibrant. Furthermore, we prove that this notion of homotopy yields a groupoid with objects being the 2-crossed module maps between two fixed 2-crossed modules (with free up to order one domain), the morphisms being the homotopies between 2-crossed module maps.
ER  -

AKCA, Ilker; Kadir EMIR a Joao Faria MARTINS. POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS. \textit{Homology, Homotopy and Applications}. SOMERVILLE: Droz, 2016, roč.~18, č.~1, s.~99-128. ISSN~1532-0073. Dostupné z: https://doi.org/10.4310/HHA.2016.v18.n1.a6.

Přehled o publikaci