We define the notion of whiskered categories and groupoids, showingthat whiskered groupoids have a commutator theory. So also dowhiskered $R$-categories, thus answering questions of what might be "commutative versions" of these theories. We relate these ideas tothe theory of Leibniz algebras, but the commutator theory here doesnot satisfy the Leibniz identity. We also discuss potentialapplications and extensions, for example to resolutions of monoids.
Journal of Homotopy and Related Structures, Vol. 5(2010), No. 1, pp. 305-318