I know what it means to be a isomorphism in a given category. But now i want to prove the following statements:
- Isomorphisms are exactly the bijections in the catgeory of Sets (Sets)
- Isomorphisms are exactly the bijective homomorphisms in the catgeory of Monoids (Monoids)
Are these facts not trivial because it is already the same definition or do i not see the difficulty in the proofs? Can someone givbe a comment/hint on this?
Thank you :)