Category type of connection is the author making between Christie and her brothers and sisters.
What is connection?
The term connection refers to the human connection to the deep bond they're feeling to each other. The connection is husband and wife, mother and and son, brother and sister, boy and girl etc.
According to the passage, the author described the category as a connection to the brother and sister between connections. The category means a word related to another word. All the brothers and sisters won the competition in first place.
As a result, the connection between the Christie and her brothers and sisters is the category.
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