7. Give an example of a category with two objects and 5 maps f, g, x,...

 

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7. Give an example of a category with two objects and 5 maps f, g, x, y, z, with f : A → A, g: A → A, x : A → B, y : B → A, z : B -→ B. Be sure to check (and give reasoning why) your category satisfies the required axioms. As we did in question #5, you can express the composition operation of your category in a table: f g y f g y However, note that in this case, not all composites are defined: for example, since the codomain of f: A→ A doesn't match the domain of y : B → A, you don't have to define the composite f;y. But you do, for example, have to define what the composite f;x is, since the codomain of f matches the domain of x (f : A A while x : A→ B). 7. Give an example of a category with two objects and 5 maps f, g, x, y, z, with f : A → A, g: A → A, x : A → B, y : B → A, z : B -→ B. Be sure to check (and give reasoning why) your category satisfies the required axioms. As we did in question #5, you can express the composition operation of your category in a table: f g y f g y However, note that in this case, not all composites are defined: for example, since the codomain of f: A→ A doesn't match the domain of y : B → A, you don't have to define the composite f;y. But you do, for example, have to define what the composite f;x is, since the codomain of f matches the domain of x (f : A A while x : A→ B).

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