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We classify braided extensions $C$ of a rank $2$ fusion category. The resultshows that $C$ is tensor equivalent to a Deligne's tensor product of some knowncategories, except $C$ is slightly degenerate and generated by a$\sqrt{2}$-dimensional simple object. To start with, we describe the fusionrules, universal grading group, and the Frobenius-Perron dimensions of simpleobjects of $C$ without the restriction that $C$ is braided.

Braided extensions of a rank $2$ fusion category