Paths

[@xanderlewis]

This is a lovely video. I had always wondered what was so special, topologically, about closed intervals. It does seem to raise the question of what’s so special about the real numbers (topologically, analytically, algebraically…), but I think that can be answered in a similar fashion by appealing to some of its natural properties and its being the unique such thing (up to isomorphism of whatever kind of thing we’re talking about) with those properties. [I think the colours at 4:00 are the wrong way around.. not that it matters…!]

[@topology_categorical]

Yes, good catch! The yellow and blue parts of the interval on the right should be the other order.

[@__-cx6lg]

2:06 What's the link to the paper? (Or an explanation of what the interval's universal property is exactly?)

[@topology_categorical]

I think this nLab article explains the universal property well: ncatlab.org/nlab/show/coalgebra+of+the+real+interval and includes links to Freyd's papers in the References.