| 1. | Likewise, monoid homomorphisms are just functors between single object categories.
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| 2. | Of course, every measurable monoid is a conical refinement monoid.
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| 3. | Of course, every measurable monoid is a conical refinement monoid.
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| 4. | A transformation monoid whose elements are invertible is a permutation group.
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| 5. | Functors between one-object categories correspond to monoid homomorphisms.
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| 6. | If an inverse monoid is cancellative, then it is a group.
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| 7. | Lists form a monoid under the " append " operation.
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| 8. | The monoid unit must then be the top element 1.
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| 9. | Applications outside of the semigroup and monoid theories are now computationally feasible.
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| 10. | Some authors regard " semigroup " and " monoid " as synonyms.
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