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Exercise 31 - Chapter 3

edited June 2018 in Exercises

Recall Examples 3.12 and 3.17. A monoid in which every morphism is an isomorphism is known as a group.

1) Is the monoid in Example 3.6 a group?

2) What about the monoid in Example 3.10a and Example 3.10a?

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Comments

  • 1.

    1) No, there are no inverses for non-identity morphisms.

    2) \(\mathcal{C}\): Yes, \(s^{-1}=s,\mathrm{id}_z^{-1}=\mathrm{id}_z\). \(\mathcal{D}\): No, there are no inverses for non-identity morphisms.

    Comment Source:1) No, there are no inverses for non-identity morphisms. 2) \\(\mathcal{C}\\): Yes, \\(s^{-1}=s,\mathrm{id}_z^{-1}=\mathrm{id}_z\\). \\(\mathcal{D}\\): No, there are no inverses for non-identity morphisms.
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