Exercise 4

Warm up Exercises

Let $+$ denote the co-product operation, and $\times$ denote products.

1. Prove directly that $A + B$ and $B + A$ are isomorphic directly without using duality.
2. Assume that $A\times B$ is isomorphic to $B\times A$, use this fact and duality to prove that $A + B$ and $B + A$ are isomorphic.
3. In the category of posets work out what the co-product of two posets would be.
4. Try to understand Example 3.9.

Exercises from the book (they are quite hard)

Chapter 3 1,2,3,6 (only for Monoids) 11 If you can understand the proof of exercise 1 you are doing well.