Publication details
POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS
| Authors | |
|---|---|
| Year of publication | 2016 |
| Type | Article in Periodical |
| Magazine / Source | Homology, Homotopy and Applications |
| Citation | |
| Web | http://dx.doi.org/10.4310/HHA.2016.v18.n1.a6 |
| Doi | http://dx.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 |
| Description | 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. |