Geodesic
Pointed homotopy of maps between 2-crossed modules of commutative algebras
Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 99-128.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2016.v18.n1.a6
Classification : 55U10, 18D05, 18D20, 55Q15
Keywords: simplicial commutative algebra, crossed module of commutative algebras, 2-crossed module of commutative algebras, quadratic derivation 
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     title = {Pointed homotopy of maps between 2-crossed modules of commutative algebras},
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İ. İlker Akça; Kadir Emir; João Faria Martins. Pointed homotopy of maps between 2-crossed modules of commutative algebras. Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 99-128. doi : 10.4310/HHA.2016.v18.n1.a6. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a6/

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