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

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

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

• Originální jazyk: angličtina
• Typ výsledku: Článek v odborném periodiku
• Utajení: není předmětem státního či obchodního tajemství
• WWW: URL
• Impakt faktor: Impact factor: 0.486
• Doi: http://dx.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

Anotace

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.