Re: Snake lemma-Five lemma

in article <1126125442.536304.237210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
ed hook <hook@xxxxxxxxxxxx> wrote:

|> But diagram-chasing requires the objects to be sets and the maps to
|> be set-maps. Invoking the Snake-Lemma gives you an element-free
|> proof of the Five Lemma, which is itself something that might be
|> useful.
|
| Well ... clearly ... I wasn't thinking along those lines. Given
| that desire for greater generality/applicability, I guess I was a
| little harsh ... :-)
|
| But that raises a question in my mind: is there an "element-free"
| proof of the Snake Lemma ??

there's a semi-famous one in maclane's "categories for the working
mathematician". but isn't there also some sort of meta-theorem
(justified by "embedding theorems" of some sort) to the effect that
"diagram-chasing proofs are perfectly valid even for arbitrary abelian
categories" (or something like that)?













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