After having understood direct limits of direct systems and inverse limits of inverse systems, as well as the corresponding categorical notions of colimits and limits, I'm left wondering why the latter are named this way and not swapped.
At least to me, it would make more sense for a "limit" to be something where the arrows come "from" a diagram (as in a direct limit), but that's a colimit.
Is there some good reason to define them this way around? If not, then how did they come to be named this way?