Bergoglio is not a valid pope. He has professed the heresy against the death penalty in Argentina

The Magisterium of the Catholic Church declares null and invalid the election of a heretic as pope. The heretic is not a member of the Church and a heretic can not be head of the Church. 

Conversations with Bergoglio, p. 101: “… there is now an increasing awareness of the immorality of the death penalty.”

He is re-endorsing the heresy by publishing the heresy again in the new edition of his book written in Argentina and endorsing it as if he was a pope; and by adulterating the Catechism Bergoglio is demonstrating his contumacy towards this heresy.