Some categorical results in the theory of crossed modules in commutative algebras (Q1089421)

Let k be a commutative ring (associative) with identity element and let R be a k-algebra. A crossed module is an R-algebra C together with an R- algebra morphism: \(\partial: C\to R\) such that \(\partial c\cdot c'=cc'\) for all c,c'\(\in C\). The paper investigates some categories of crossed R- modules, crossed complexes and chain complexes and studies the existence of adjoints between such categories.