Publication details
TWO-FOLD HOMOTOPY OF 2-CROSSED MODULE MAPS OF COMMUTATIVE ALGEBRAS
Authors | |
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Year of publication | 2019 |
Type | Article in Periodical |
Magazine / Source | Communications in Algebra |
MU Faculty or unit | |
Citation | |
Web | http://dx.doi.org/10.1080/00927872.2018.1476523 |
Doi | http://dx.doi.org/10.1080/00927872.2018.1476523 |
Keywords | 2-crossed module of commutative algebras; crossed module of commutative algebras; quadratic derivation; simplicial commutative algebra |
Description | 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. |