2024-12-06

This following is a very brief summary of what happened in class on 2024-12-06.

We began by recalling the donor and receptor objects, as well as the Salamander Lemma. We noted how the Salamander Lemma allows us to deduce situations in which the extramural maps are isomorphisms, as well as (more intricate) situations in which the intramural maps are isomorphisms.

We then used the Salamander Lemma to sketch "quick" proofs of both the Four Lemma (of which the Five Lemma is an immediate consequence) and the famous Snake Lemma. We didn't have time to cover ever detail, but we did see how a zig-zag of extramural isomorphisms, capped off with intramural isomorphisms, allowed us to deduce each result.

THE END.

Concepts

• The Salamander Lemma
• Diagram lemmas

References

• You are now a living reference.