Is the long line a colimit in a suitable category, if not in $\mathbf{Top}$?

Question

The only definitions of the so-called long line I've encountered so far all consist, with only slight variations, in forming a long ray by means of the lexicographical order on $\omega_1\times[0,1)$, where $\omega_1$ denotes the smallest uncountable ordinal, and then glueing two long rays at the origin, which to my knowledge is a totally sui generis manner of constructing anything, in particular what turns out to be a rather interesting manifold, so I'm wondering, on the one hand, if there are radically distinct definitions of the long line, specially if there's some definition in terms of a colimit, which sounds more plausible to me, or maybe even a limit if it happens to work, if not in the category of topological spaces with or without some extra assumptions, at least in some suitable category, but preferentially not one baked specifically for that purpose, and, on the other hand, if there are other interesting mathematical objects, possibly in set theory, whose definition somehow resembles the one mentioned above.