John wrote:

>I should warn people that I've fixed my convention concerning the cap: now it's

>$\cap_X \colon \textbf{1} \nrightarrow X \times X^{\text{op}}$

So for this cap, we have \$$\cap_X (x,x') = \hom(x',x) = \cup_X (x,x')\$$ ??

This doesn't seem arbitrary to me for some reason. The new cap bends upwards so when you combine it with a cup you get a snake but the old cap bends downwards which produces a loop when combined with a cup?

This is pure newb rambling but the snake seems like an identity on a wire whereas the loop is an identity on a box...