In the joint statement, the two orders said that their task was the "spiritual and temporal conquest" of the "vast territory" called California. They also referred to themselves as being "in this corner of the world of Old and New California, occupied with the spiritual conquest and conversion of the infidels." Infidels translates to "not of the faith," or, in other words, non-Catholic.
Conquest is one aspect of the paradigm of domination that underlies the colonizing mission of the Vatican and the Catholic Church in the Americas, in keeping with papal decrees that called for the "subjugation" of "barbarous nations." As part of this charge, one task of the church was to break the free spirit of and "reduce" those who were "not of the faith." Spiritual conquest involved the use of spirit-breaking techniques that served as part of the arsenal that was employed against the originally free and independent Indian nations and peoples of California.