MathOverflow

I recently watched a numbers show, and one of the acts was number mind reading. It went like this:Take a positive integer n and reverse it, we define this as R(n), and take the absolute value of n minus R(n), we define this as F(n). The magician will...

The standard concatenation of loops and paths is not associative. As I seem to know from "folklore", Moore solved this problem by introducing spaces of measured paths and loops.
There are a bunch of important basic facts about these things -- they are equivalent to the standard spaces, etc. -- and I've checked them all, but in my writing, I would like to have a nice reference for this basic theory. (To save space, and to give...

There are many categories which are not regular by essentially the same counterexample, namely, Example 3.14 at the nLab article on regular categories. It is an example of a regular epi which is not pullback-stable, and it works for $\mathbf{Pos}$, ...

Let
$$U:E\to S,\qquadU’:E\to T$$
be functors, and suppose that the right Kan extension