Why double categories? Part 1

Lately I’ve been fixated on double categories, pursuing a range of theoretical and applied directions. Being a type of higher-dimensional category, double categories might seem intimidating, especially to newcomers to category theory. So I’d like to explain what makes double categories so natural, even inevitable.

This is a companion discussion topic for the original entry at https://topos.site/blog/2024-01-15-why-double-categories-part-1/