Peter Freyd's recent posting of the `Categories Anonymous' skit prompted me to dig out and transcribe an even older skit which originated with the Chicago Junior Math Club, and which stars Saunders Mac Lane as the evil villain Chalkfinger. I don't know its exact date: it should be datable by the reference at the end to Chalkfinger's visit to Japan, but although Saunders refers to that visit in his autobiography (p. 297) he doesn't quote the date. The typescript copy which I have (and which I acquired from Murray Adelman in 1984) was apparently revised for performance at the Bowdoin Summer Advanced Seminar in Homological Algebra (again, I don't know the year). If anyone knows more details of the history of the skit, I'd be interested to hear them. Peter Johnstone ++++++++++++++++++++ DRAMATIS PERSONAE: K.: Kaplansky Chestcough: Ann Chertkoff (secretary) Bailout: Baily Bond: Herstein Chalkfinger: Mac Lane Manishevitz: Liulevicius Filterfish: Amitsur Oddprime: Applied Math (?) Pedro: Calderon Ziggy: Zygmund Browser (Felix) Browder SCENE 1 Opening: [Goldfinger theme heard. Jacobson writes on blackboard] Jacobson: Good evening, welcome to the Junior Math Club's presentation of Chalkfinger. [He is dragged off. A scream is heard offstage,] [Desk of K, chair for Miss Chestcough] K: Miss Chestcough! Chest: [cough] Yes? [Bailout runs in.] Bailout: Who coughed? Chest: Me, Professor Bailout. Bailout: Well, don't let it happen again. [exit] Chest: {aside] That was a young right idealist. K: Miss Chestcough, see if you can get Agent 00\pi on the red telephone. Chest: At 8.30 in the morning? Well, I'll try K., but 00\pi is always so irrational at this hour. [exits to call] K: Hmmm. How does she know that? [Chestcough returns, after a minute Bond enters] Bond: [flirting] Hello, pigeon. Why do I chase around the world when there are girls like you at home? Chest: [smiles] You'd better go in to see K., but I'll be here when you get back. [Bond crosses to K.'s desk, sits down. K. stares at him for *long* moment.] K: Could you give me an epsilon of your time? Bond: Make it epsilon over 2. What's up, Boss? K: Well, it's Chalkfinger. He's been at our chalk supply again. Why, that man is responsible for most of the world's illicit traffic in colored chalk. Bond: But what does he use it for? K: You won't believe this. He proves theorems about categories! Bond: [laughs] That's ridiculous! [does double-take] What's a category? K: Why, don't you know? You're not up with the times, Bond. As I understand it, categories arose from Pavlov's experiments with dogs. Pavlov trained dogs to expect meat at the sound of a bell. Then he took the meat away, but the dogs continued to salivate when the bell was rung. Now Chalkfinger has taken the meat out of mathematics, but mathematicians still salivate at the sound of the bell. Bond: Insidious! K: You bet. Now I want you to infiltrate their organization. Bond: But suppose I don't make the grade? K: You'll do it, Yitz. I'm putting my money on Israel Bond. Bond: Thank you, sir. I'll try to protect your interest. Say, whatever happened to that last case you were working on? K: I couldn't get anywhere on it, so I turned it over to a graduate student. Now, for your equipment: [they stand up] We've prepared for you a white Jaguar complete with left and right annihilators, deformation retract and portable pool table. Here's the key to the locked stall in the third floor john. We'll communicate as usual by leaving messages under the seat. Use all the paper you want, and good luck! [Exeunt -- Alperin and Thompson make first crossing of stage] SCENE 2 [Students playing chess] Student 1: Going to the colloquium today? All the big operators from Spectrum are going to be there: Big Ziggy, Big Pedro and even Big Browser, their [gestures] elliptic operator. Student 2: Nah, I'm too busy playing chess. Student 1: Oh, Chalkfinger won't like that. [long pause -- Chalkfinger enters with Oddprime] Chalk: By thunder, you know what can happen to students like you? Oddprime! Hat! [Oddprime throws frisbee, something breaks] Chalk: Hah, Oddprime can divide anything. [Bond enters] Welcome to our organization, Mr Bond. We're looking forward to your course in Hopf algebras. Let me show you around. Manishevitz, here, is working on a computer program to determine the first odd square. Manish: My name is Manishevitz, but you can call me Manishevitz if you want. Bond: That looks like difficult work. Manish: Any child in first grade could do it. It's all a matter of gamesmanship. Chalk: Good man to talk to, Bond, if you can get through the queue at his door. Over there is Filterfish, still trying to disprove that the Arabs invented algebra. Filter: [whispers] What is the password? Bond: Ultra-filter. Filter: You must be the man from K. Bond: Your image is my kernel, Daddy-O. Filter: Exactly. Chalk: Mr Bond, do you subscribe to the Dieudonne doctrine or the category of vector spaces? Bond: Category, shmategory, I don't go for that crap. Chalk: Categories crap? The man's a spy! Seize him! [all seize him] What do we do with spies? Manish: We could boil him to death in Eckhart 312. Filter: Or make him teach Math 101. Chalk: I know, we'll put him trough the pull-back. Oddprime: Heh, heh, heh, through the push-out and the pull-back! All: Through the pull-back! [They drag Bond out] Bond: You may torture my body, but you'll never annihilate my ideals. [Screams heard offstage, they bring back his unconscious body and throw it on the floor. Oddprime stands guard. Pussy enters] Pussy: Izzy dead? Oddprime: No, Izzy just tired. [Bond rises slowly, shakes himself] Bond: Well, hello. Pussy: Hi! My name is Pussy Galois. Bond: [half-fainting again] Wow, are you ever projective! Pussy: Not only that, I'm free. Bond: [stands up] I'd like to prove that. Pussy: It's been tried before but [sitting down] maybe your techniques are better. Bond: [joining her] Say, Pussy, how does Chalkfinger smuggle his chalk out of the building? Pussy: Oh, haven't you ever figured that out? He hides it in his baggy pants. Bond: Ingenious! [Alperin and Thompson make second crossing] Bond: What in the world? Pussy: Oh, they always do that. Come with me: [takes his hand] we'll eavesdrop on Chalkfinger's meeting with Spectrum. SCENE 3 [Ziggy, Pedro and Browser on stage] Pedro: What'cha got there, Big Ziggy? Ziggy: It's Chalkfinger's latest masterpiece, which I've acquired at considerable expense Pedro: Let's see: [reads] 'In the beginning Chalkfinger created the category and the functor, but the category was void and the functor was forgetful. And Chalkfinger said "Let there be maps", and there were maps. And Chalkfinger called the maps morphisms, and the members of the category he called objects, and Chalkfinger thought that was pretty good, and so did his friend Sammy. And there was evening and there was morning in 1945.' Ziggy: This beats analysis. Browser: Sounds like a very theological subject. [takes the book] 'And on the sixth day, Chalkfinger created mathematicians and set them to work in the categories' -- oh, surely that's going too far! Pedro: Shh! Here he comes. [Chalkfinger and Lin Ton enter] Chalk: Gentlemen, meet my Chinese assistant Lin Ton. I never understand you analysts, so I've brought along Lin Ton to interpret for me. Lin Ton: Have you brought the shipment? Pedro: Yes, it's all here. [They deposit chalk in a box] We had some trouble, though. Bailout keeps destroying the red chalk. Ziggy: I notice you keep the colored chalk in a separate box. Lin Ton: Separate but equal. Browser: Maybe we can integrate it while we're here. Chalk: You know, I had the strangest dream last night. I dreamed that I was surrounded by seven lean sheaves and seven flabby sheaves, and the seven lean sheaves came and devoured the seven flabby sheaves. Pedro: A singular dream! Ziggy: I think you need a different kind of analyst. Browser: Yeah, now look, Chalkfinger. We've all made our deliveries of colored chalk. You promised us that your categories would yield us theorems. This is Ext-Tor-tion! Chalk: Gentlemen, I wouldn't dream of going back on a promise. If you want, I'll give you a theorem apiece; but first I will demonstrate my new secret weapon. Pedro: Is he on the level? Ziggy: I don't know. It's hard to take the measure of the man. Chalk: You are about to witness the power of the Grothendieck ring! [Pulls out ring] Lin Ton: That ring is nil, try this one. Browser: With that ring, I thee dread. Chalk: You'd better ... [pushing him away] because none of you are getting out of here alive! [He runs offstage] [Hissing noises heard from left and right] Lin Ton: Oh no, it's the thermostats! Ziggy: Poison gas. Browser: [on left] Ahh, I'm being annihilated on the left! Pedro: [on right] And I on the right! [All collapse; Chalkfinger appears in front] Chalk: [aside] Hah, a swift death for a Swift Professor. Bond: I saw the whole thing, Chalkfinger. Your heinous crimes will not go unpunished. [Chalkfinger trips Bond, they fall, the ring slides away] Pussy: The Grothendieck ring -- it's going to explode! [Explosion noise, chairs overturned, everybody collapses] [Alperin and Thompson make final crossing, oblivious to everything] [Bond gets up, brushes himself off] Bond: Good thing I'm immune to radical rings! And so the tragic tale fo Chalkfinger comes to its untimely end. The explosion of the Grothendieck ring was powerful enough to cast Chalkfinger all the way to Japan. Because of this affair, K. had to hide out in England for a year, and I've earned an extended vacation on the Mediterranean. FINIS