| 11. | In other words, a monoid is a semigroup with an identity element.
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| 12. | However, not every monoid sits inside a group.
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| 13. | A semigroup homomorphism between monoids preserves identity if it is a monoid homomorphism.
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| 14. | Particularly, if f is surjective, then it is a monoid homomorphism.
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| 15. | However this quotient itself is generally only a monoid.
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| 16. | Those axioms are formally similar to the monoid axioms.
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| 17. | A civil war erupts between the two Monoid factions.
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| 18. | An abstract mathematical foundation for synchronization primitives is given by the history monoid.
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| 19. | The collection of functions f _ i together with composition form a monoid.
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| 20. | Since the monoid is finite, for some.
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