(Anton Geraschenko) The Salamander lemma

Secret Blogging Seminar

[I’m happy to introduce Anton, our very first guest blogger.]

A couple of years ago, George Bergman gave me a copy of a fun preprint that he never got around to preparing for publication. A scan of it is posted here. It starts

The “magic” of diagram-chasing consists in establishing relationships between distant points of a diagram—exactness implications, connecting morphisms, etc.. These “long” connections are in general composits of “short” (unmagical) connections, but the latter, and even the objects they join, are frequently not visible in the diagram-chasing proof. We attempt to remedy this situation here.

If you don’t like diagram chases, it’s likely that you still won’t like them once you know the Salamander lemma. The salamanders chase the diagrams for you, but you still have to chase the salamanders. I think the salamander proofs are easier to explain (once you know the Salamander lemma), and it’s easier…

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