# Joke explanation: "a comathematician is a device for turning cotheorems into ffee"

Ok, so apparently there is an old joke (which I DO get) that says that in Hungary a mathematician is a device for turning coffee into theorems.

I found a post by Qiaochu Yuan that has the following definiton: A comathematician is a device for turning cotheorems into ffee.

Apparently this is a very funny joke. Could someone explain it to me and tell me where I could learn about the subject in question? Thank you very much in advance.

Regards.

• That's an old joke. Perhaps you should read about limits and colimits, it might help understand it. Aug 16 '14 at 19:27
• The general joke is that given a map $f:X\to Y$, you can make a 'co' map $\text{co}f:\text{co}X\to\text{co}Y$. In this case, $\text{mathematician}:\text{coffee}\to\text{theorems}$ yields $\text{comathematician}:\text{cotheorems}\to\text{cocoffee}$. But of course coffee is just co-ffee so co-co-ffee is ffee. Aug 16 '14 at 19:30
• @IanColey Should be $\operatorname{co} Y\to \operatorname{co} X$.
– user147263
Aug 16 '14 at 19:42
• Every nut is a coconut. Aug 17 '14 at 5:59
• @900sit-upsaday, I'm not sure I agree. Given a product-preserving functor $\mathbf{C} \rightarrow \mathbf{D}$, we get a coproduct preserving functor $\mathbf{C}^\mathrm{op} \rightarrow \mathbf{D}^\mathrm{op}$. There is no switching. Aug 17 '14 at 6:00