The symmetric center of a braided category B consists of all objects of B having symmetric braiding with every object of B. The categorical Witt group W(E) of braided fusion categories with the same symmetric center E is obtained as the quotient of the monoid of such categories by its submonoid consisting of Drinfeld centers. I will discuss the structure of this group and its role in the study of minimal non-degenerate extensions of braided categories. This theory has applications to the classification of braided fusion 2-categories (which, in turn, lead to 4-dimensional TQFTs).