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# Exercise 20 - Chapter 3

edited June 2018

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

• Options
1.
edited June 2018

$$G_1$$: $$f = g$$

$$G_2$$: 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 
• Options
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.