  A representation of an object in a category is an abelian group in the
corresponding comma category. In this paper we derive the formulas describing
linear representations of objects in the category of formal loops and apply
them to obtain a new approach to the representation theory of formal Moufang
loops and Malcev algebras based on Moufang elements. Certain 'non-associative
Moufang symmetry' of groups is revealed.
