How Does XGBoost Handle Multiclass Classification?

XGBoost, LightGBM, or CatBoost are libraries that share (by default) the same kind of underlying model: decision trees. These decision trees are combined iteratively, using Gradient Boosting. I.e. the addition of new nodes to the current tree is done so that a non-linear objective, usually the squared error, is optimized. To handle the non-linearity, the objective is linearized using its Gradient and Hessian. As a reminder, the prediction process is relatively simple: given a row of data, each decision tree of the ensemble is browsed.