Snake Lemma (a VERY COMPLETE proof)

On the web, there seems to be no video giving a complete detailed proof of the celebrated Snake Lemma. We made this video to fill that hole. Myself (aBa Mbirika) and my two former students, Quotes (Katie Henschell) and Knit Mama (Taylor Kriesel), made this video a few days AFTER they both graduated from University of Wisconsin-Eau Claire. Instead of leaving Eau Claire and celebrating post-college life, they joyously studied the Snake Lemma and spent 4 or 5 hours making this video with me (which Quotes distilled to a simple 1hr 31min 19sec length using her amazing video-editing expertise). WARNING: If you are a student, please do not use this video to simply copy the proof. Attempt the proof of the different parts of this video on your own before watching each corresponding section here. To that end, here is a "clickable" table of contents for those of you who want to skip around to specific parts of the proof. INTRODUCTION: Names/introduction (Everyone) - 0:00 What is the snake lemma? (aBa) - 0:56 Defining the maps (aBa) - 2:29 What we want to show (Everyone) - 5:21 PART 1: i bar and j bar are well defined (Quotes) - 7:14 PART 2: i prime bar and j prime bar are well defined (Knit Mama) - 9:52 PART 3: constructing the connecting homomorphism delta (aBa) - 13:02 delta is well defined (aBa) - 20:10 PART 4: 4a) Exactness at ker g (Quotes and Knit Mama) - 31:05 image of i bar is subset of ker of j bar (Quotes) - 31:36 aBa notices Jimi Hendrix in the proof (Guitar Solo) - 34:01 image of i bar is superset of ker of j bar (Knit Mama) - 34:14 4b) Exactness at ker h (aBa) - 37:32 image of j bar is subset of ker of delta (aBa) - 37:59 picture to motivate proof (aBa) - 40:25 aBa shows his super-speed drawing ability - 40:35 to 41:08 proof begins (aBa) - 43:45 image of j bar is superset of ker of delta (aBa) - 47:54 picture to motivate proof (aBa) - 48:50 proof begins (aBa) - 54:30 4c) Exactness at coker f (Quotes and Knit Mama) - 1:03:32 image of delta is subset of ker of i prime bar (Knit Mama) - 1:03:55 image of delta is superset of ker of i prime bar (Quotes) - 1:06:10 picture to motivate rest of Quotes' proof (aBa) - 1:09:28 conclusion of Quotes' proof (Quotes) -1:10:57 4d) Exactness at coker g (aBa) - 1:11:35 image of i prime bar is subset of ker of j prime bar (aBa) - 1:11:50 aBa notices Jimi Hendrix AGAIN in the proof (Guitar Solo) - 1:13:13 image of i prime bar is superset of ker of j prime bar (aBa) - 1:17:52 aBa, Quotes, and Knit Mama get loopy due to LONG proof duration - 1:24:40 conclusion of part 4d proof (aBa) - 1:25:40 CONCLUSION: Wrapping up (Everyone) - 1:29:02 Showing all our proofs (Everyone) - 1:29:46 If you have any questions/comments about this proof or anything at all, please feel free to post your thoughts in the comments. Or feel free to email me (aBa) at [email protected]