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

AKCA, Ilker, Kadir EMIR and Joao Faria MARTINS. POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS. Homology, Homotopy and Applications. SOMERVILLE: Droz, 2016, vol. 18, No 1, p. 99-128. ISSN 1532-0073. Available from: https://dx.doi.org/10.4310/HHA.2016.v18.n1.a6.

Basic information

Original name

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

Authors

AKCA, Ilker, Kadir EMIR and Joao Faria MARTINS

Edition

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

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Other information

Language

English

Type of outcome

Článek v odborném periodiku

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.486

DOI

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

UT WoS

000383324400006

Keywords in English

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

Tags

RIV ne

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Abstract

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.