9
$\begingroup$

How can I prove that additive functors preserve split exact sequences?

  • 6
    Prove that a split exact sequence $0 \to A \to B \to C \to 0$ is isomorphic to the obvious direct sum sequence $0 \to A \to A \oplus C \to C \to 0$.2012-04-18
  • 8
    (Prove also that a functor is additive if and only if it preserves 0 and binary direct sums.)2012-04-18
  • 0
    @ZhenLin Please consider converting your comment (and the comment by t.b.) into a (hint only) answer, so that this question gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868).2013-06-18

1 Answers 1