Categories via path equations

We can add constraints to a free category which states that two paths are equal

Exercise 3-17(2)

Write down all the morphisms in the free category presented by the following diagram:

Solution(1)

A,B,C,D,f,h,g,i,j

Exercise 3-19(2)

What are the morphisms in the following category: \(\boxed{\overset{\bullet}{z}\circlearrowleft s\ \ \boxed{s;s;s;s = s;s}}\)

Solution(1)

z,s,ss,sss