topoology @topoology@mathstodon.xyz

I must admit that the my first #topoology breakthrough was conceived under the influence of a bidet.

I have since bought a Japanese toilet with one of these magical theorem fountains. The previous owner: Shinichi Mochizuki. Coincidence? I think not. What else could have revealed to him the relationship between set theory and the fiber functor?

An oft overlooked fact: implicit in the saying "a mathematician is a machine for turning coffee into theorems" is that the more theorems you prove, the more intimately familiar you must be with your toilet.

Topoology can make one feel a bit mathematically constipated at times - but sometimes all you need to do is push it out.

\(
\require{AMScd}
\begin{CD}
\unicode{x1f4a9}_A @>{i}>> \unicode{x1f4a9}_L\\
@VV{f}V @VV{\Phi\unicode{x1f4a9}_L}V \\
\unicode{x1f4a9}_F @>{\Phi\unicode{x1f4a9}_F}>> \unicode{x1f4a9}_F \cup_f \unicode{x1f4a9}_L
\end{CD}
\)

If the above diagram is commutes, we have a pushout! All you're doing is gluing poops together to create adjunctive poops. Potty training.

#topoology

Brownhead's theorem tells us that asspherical poops have contractible universal covers.

It follows that all compact orientable deuces are asspherical, as long as their genus is greater than 0.

The Hind-Bowel theorem states that a subset of a Euclidean poop is compact if and only if the toilet lid can be closed and bounded

#topoology