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I.e. I want to put in Baseball and get out Sports & Outdoors.

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Try WordNet.

The relation beween Baseball and Sports is called hypernym.

Here is a snippet out of WordNet's baseball hypernym hierarchy:

S: (n) baseball, baseball game, ball (a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs) "he played baseball in high school"; "there was a baseball game on every empty lot"; "there was a desire for National League ball in the area"; "play ball!" direct hyponym / full hyponym domain term category direct hypernym / inherited hypernym / sister term S: (n) ball game, ballgame (a field game played with a ball (especially baseball)) S: (n) field game (an outdoor game played on a field of specified dimensions) S: (n) outdoor game (an athletic game that is played outdoors) S: (n) athletic game (a game involving athletic activity) S: (n) sport, athletics (an active diversion requiring physical exertion and competition) S: (n) diversion, recreation (an activity that diverts or amuses or stimulates) "scuba diving is provided as a diversion for tourists"; "for recreation he wrote poetry and solved crossword puzzles"; "drug abuse is often regarded as a form of recreation" S: (n) activity (any specific behavior) "they avoided all recreational activity" S: (n) act, deed, human action, human activity (something that people do or cause to happen) S: (n) event (something that happens at a given place and time) S: (n) psychological feature (a feature of the mental life of a living organism) S: (n) abstraction, abstract entity (a ...

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