COMMUNICATIONS IN ALGEBRA, vol.47, no.1, pp.289-311, 2019 (SCI-Expanded)
Article / Article
COMMUNICATIONS IN ALGEBRA
Science Citation Index Expanded (SCI-EXPANDED), Scopus
2-crossed module of commutative algebras, crossed module of commutative algebras, quadratic derivation, simplicial commutative algebra, POINTED HOMOTOPY, HOMOLOGY
Eskisehir Osmangazi University Affiliated:
We address the homotopy theory of 2-crossed modules of commutative algebras. In particular, we define the concept of a two-fold homotopy between a pair of one-fold homotopies connecting 2-crossed module maps . We also prove that if the domain 2-crossed module is free up to order one (i.e., if the bottom algebra is a polynomial algebra) then we have a 2-groupoid of 2-crossed module maps and their homotopies and two-fold homotopies.