Answer:
The answer to the question: These outposts were established in Spanish colonies - either along the coast or in remote areas - to spread Catholicism among the native cultures, would be: Missions.
Step-by-step explanation:
After Christopher Columbus discovered the Americas in 1492, and as the Spanish started colonizing the territories and came into contact with the Native American tribes resident in these parts, one of the driving motivations the Spanish Crown had was to Evangelize these people considered as pagans, and turn them into converts of Catholicism. This is why Christian missionaries, of different Catholic congregations, first of which was Pedro de Gante, a Franciscan, and others like him, arrived in the Americas in 1523, and comissioned by the Spanish Crown, started what is known as the missions, outposts that went from current day U.S territories to Chile and Argentina, and whose purpose was to civilize the Indians through the learning of language, European traditions, and most of all, through conversion to the Catholic faith.