Groups With Additional Structure
Many groups are simultaneously groups and examples of other mathematical structures. In the language of category theory, they are group objects in a category, meaning that they are objects (that is, examples of another mathematical structure) which come with transformations (called morphisms) that mimic the group axioms. For example, every group (as defined above) is also a set, so a group is a group object in the category of sets.
Read more about this topic: Group (mathematics)
Famous quotes containing the words groups, additional and/or structure:
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—Philip Larkin (1922–1986)
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—Ambrose Bierce (1842–1914)
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—Sarah Patton Boyle, U.S. civil rights activist and author. The Desegregated Heart, part 2, ch. 2 (1962)