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 Post subject: Category Theory for beginners (3)Posted: Sat Jan 16, 2016 11:18 pm
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Joined: Tue Nov 10, 2015 8:25 pm
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Let $\displaystyle f : M \longrightarrow N$ be an $R$-module homomorphism. Identify each $R$-module homomorphism in each of the following sequences and then show that each sequence is exact.

1. 0 $\rightarrow$ $\displaystyle \ker (f)$ $\rightarrow$ $M$ $\rightarrow$ $\displaystyle Im(f)$ $\rightarrow$ 0
2. 0 $\rightarrow$ $\displaystyle Im(f)$ $\rightarrow$ $N$ $\rightarrow$ $\displaystyle Coker(f)$ $\rightarrow$ 0
3. 0 $\rightarrow$ $\displaystyle \ker (f)$ $\rightarrow$ $M$ $\rightarrow$ $N$ $\rightarrow$ $\displaystyle Coker(f)$ $\rightarrow$ 0

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