Hi, how is it defined the normalization of an algebraic stack $A$ inside another algebraic stack $B$. If you do not want to write the answer could you give to me some reference? Thank you
To define the normalization of $A$ in the absolute setting (i.e. no stack $``B"$), one can use 2-universal property. Note that since normality is local for the smooth topology, we know what a normal algebraic stack means: it is normal if it has a presentation which is a normal scheme. To construct it we follow Mattia's comment.
For the relative setting, I don't quite understand, but I guess you mean there is a given morphism $B\to A.$ Do you want it to be representable?