All paired muscle systems are represented in the brain by paired controlling centres. Dominance, or leading control of the function, may be entirely leftsided, in which case the organs controlled are dominant on the right side, or entirely right-sided. If some centres are on the left and some on the right side of the brain, the condition is called crossed laterality. The dominance may be fixed,...

‎We firstly prove the completeness of the category of crossed modules in a modified category of interest‎. ‎Afterwards‎, ‎we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows‎. ‎These constructions unify many corresponding results for the cases of groups‎, ‎commutative algebras and can also be adapted to ...