Thus, the Maya people spoke the Mayan language. Today, in normal American usage, Mayan is accepted as the adjective, though scholars prefer to keep to the word Maya. The Maya people built fabulous Maya pyramids while speaking Chol Mayan language with some influence from Yucatec Maya language. These are separate Mayan languages, not dialects. The word archaeology can be spelled, and mis-spelled a variety of ways, such as archeology.
Archaeology is a sub-discipline of anthropology, as are ethnography and ethnology.
Often these are grouped with the Social Sciences, often with the Humanities. Obviously the arts come into play as well, since the Aztec, Olmec, Mixtec, Maya, Zapotec, Toltec, Teotihuacan, West Coast Mexico, and other prehispanic civilizations produced all kinds of art, murals, sculpture, stelae, pottery, and monumental architecture. Their most famous buildings are temples, pyramids, palaces, ball courts, and sweat baths. In the beginning archaeology was a search for buried treasure, tombs, and gold, or in the case of the Maya, for jade and polychrome painted vases. Nowadays it is a search for knowledge that keeps most archaeologists going.