On the braiding of an Ann-category

A braided Ann-category $\text{A}$ is an Ann-category $\text{A}$ together with the braiding $c$ such that $(\text{A},\otimes ,a,c,(I,l,r))$ is a braided tensor category, and $c$ is compatible with the distributivity constraints. The paper shows the dependence of the left (or right) distributivity constraint on other axioms. Hence, the paper shows the relation to the concepts of {\it distributivity category} due to M. L. Laplaza and {\it ring-like category} due to A. Frohlich and C.T.C Wall. The center construction of an almost strict Ann-category is an example of an unsymmetric braided Ann-category.