Does a Catholic bishop appoint the Canon priests of his cathedral? I hope to learn whether the Prebendary Agustín Fernández de San Vicente became Canon of the Durango Cathedral because he was appointed by Bishop Castañiza of Durango or for some other reason.

Fernández was previously chaplain of the naval company at San Blas and before that, priest of Tamazula, Nueva Vizcaya.
The short answer to this question is possibly.


  Manner of appointment
  
  As only the Holy Father can erect a chapter, so also he alone has power to appoint the individual members of a chapter. This power may be, and in fact is delegated, and hence canons are appointed sometimes by the pope, sometimes by the bishop or the capitular body, sometimes by others to whom the right has been given. By the rules of the Roman Chancery all prebends which become vacant in curia (i.e. when one who holds a benefice dies in Rome) are reserved to the Holy See, also the appointment to a vacant prebend the former holder of which has been deprived of it by an act of the Holy See, the appointment of the first dignitary of each chapter, and to all other prebends which become vacant during the months of January, February, April, May, July, August, October, and November. Beyond this the law does not expressly state in whom resides the power to collate to cathedral canonries and prebends, but the general opinion is that the right is invested simultaneously in the bishop and chapter; therefore for a valid election the majority of the canons must agree with the bishop when a new appointment is made. Exceptions are made in the following cases: if from the foundation of the church or benefice the appointment belongs to a particular person; if there is an immemorial custom to the contrary; the appointment of the canon theologian and the canon penitentiary; the canons in France (Deshayes, Memento Juris Eccl., 3d ed., Paris, 1903). Appointment is practically always made by letter, and possession of a canonry cannot be obtained until the nominee presents his letter of appointment. The Council of Trent orders that on the day of taking possession, or at least within two months, the new canon is to make his profession of faith and also obedience to the bishop. This profession of faith is made to the bishop himself or, if he be absent, to the vicar-general or another delegated for this purpose. The profession of faith must be made in presence of the chapter, otherwise the new canon may be deprived of possession and the prebendal fruits and daily distributions. - Canon (Catholic Encyclopedia)