I am reading about split exact sequence and come out with a question. Consider the following sequence.
$0 \to A\to A\oplus B\oplus C\to B\to0$
It seems to me that it's exact. So, is it an split exact sequence?
To be more explicit, just set $A\to A\oplus B\oplus C$ to be $a\to (a,0,0)$, and $ A\oplus B\oplus C\to B $ to be $(0,b,0)\to b$.