In Daniele Turi's "Category Theory Lecture Notes" from the University of Edinburgh, shouldn't "cone" be "cocone" in the definition of a colimit?
A generic arrow $\tau : J\Rightarrow \Delta Y$ from $J$ to $\Delta$ is then a cone under $J$ consisting of a vertex $Y$ (which is an object of $\mathbb{C}$) and one arrow $$\tau _{B}: JB\to Y$$
$\dots$ and so on.
The reason I ask is that in "Abstract and Concrete Categories: The Joy of Cats," by Adámek, Herrlich, and Strecker, a cone is defined as a natural source, which (I think) is the other way around . Is it because of the "under $J$"?
