My current impression is that broader adoption of category theory is limited in large part by bad definitions, even when more intuitive equivalent definitions are available—“morphisms” vs “paths”
Just wanted to note that I recently learned some of the very basics of category theory and found myself asking of the presentations I came across, “Why are you introducing this as being about dots and arrows and not immediately telling me how this is the same as or different from graph theory?”
I had to go and find this answer on Math.StackExchange to explain the relationship, which was helpful.
So I think you’re on the right track to emphasize paths, at least for anyone who knows about graphs.
Just wanted to note that I recently learned some of the very basics of category theory and found myself asking of the presentations I came across, “Why are you introducing this as being about dots and arrows and not immediately telling me how this is the same as or different from graph theory?”
I had to go and find this answer on Math.StackExchange to explain the relationship, which was helpful.
So I think you’re on the right track to emphasize paths, at least for anyone who knows about graphs.
I also liked the explanation of natural transformations as being about prisms, I found that image helpful.