Akça, I. IlkerEmir, KadirMartins, João Faria2018-07-192018-07-1920161532-0073PURE: 5465365PURE UUID: 88c0bbf2-5644-4091-80ab-2d7376122ae6Scopus: 85046671254WOS: 000383324400006http://www.scopus.com/inward/record.url?scp=85046671254&partnerID=8YFLogxKJFM was partially supported by CMA/FCT/UNL, under the project UID/MAT/00297/2013 and by FCT (Portugal) through the "Geometry and Mathematical Physics Project", FCT EXCL/MATGEO/0222/2012. KE expresses his gratitude to CMA for the hospitality in 2014/15. We would like to thank Ronald Brown for useful comments and several corrections.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.30353760eng2-crossed module of commutative algebrasCrossed module of commutative algebrasQuadratic derivationSimplicial commutative algebraMathematics (miscellaneous)journal article10.4310/HHA.2016.V18.N1.A6https://www.scopus.com/pages/publications/85046671254