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# Exercise 39 - Chapter 3

edited June 2018

Consider the free categories $$C = [ \cdot \rightarrow \cdot ]$$ and $$D =[ \cdot \rightrightarrows \cdot ]$$ . Give two functors $$F, G : \mathcal{C} \rightarrow \mathcal{D}$$ that act the same on objects but differently on morphisms.

Both $$F: C \to D$$ and $$G: C \to D$$ can map the left point to the left point, and the right point to the right point. But they can differ by having $$F$$ map the one morphism in $$C$$ to the top morphism in $$D$$ and having $$G$$ map the one morphism in $$C$$ to the bottom morphism in $$D$$.
Comment Source:Both \$$F: C \to D\$$ and \$$G: C \to D\$$ can map the left point to the left point, and the right point to the right point. But they can differ by having \$$F\$$ map the one morphism in \$$C\$$ to the top morphism in \$$D\$$ and having \$$G\$$ map the one morphism in \$$C\$$ to the bottom morphism in \$$D\$$.