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Exercise 20 - Chapter 3

What equations would you need to add to the graphs below in order to present the associated preorders?

diagram

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Comments

  • 1.
    edited June 11

    \(G_1\): \(f = g\)

    \(G_2\): None (I think)

    \(G_3\): \(f.h = g.i\)

    \(G_4\): None

    Comment Source:\\(G_1\\): \\(f = g\\) \\(G_2\\): None (I think) \\(G_3\\): \\(f.h = g.i\\) \\(G_4\\): None
  • 2.

    For \(\mathcal{G}_2\), shouldn't we impose \(f\) to be the identity morphism, that is \(f = 1\)? Otherwise, there are infinitely many morphisms from \(\bullet\) to \(\bullet\): \(1, f, f \circ f, f \circ f \circ f\), etc.

    Comment Source:For \\(\mathcal{G}_2\\), shouldn't we impose \\(f\\) to be the identity morphism, that is \\(f = 1\\)? Otherwise, there are infinitely many morphisms from \\(\bullet\\) to \\(\bullet\\): \\(1, f, f \circ f, f \circ f \circ f\\), etc.
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