Bah
I don't understand why people ever say things in math without accompanying them with an explanation of what's actually going on in them. It's just so...why???
(Specifically, this was prompted by thinking about the fact that a simplicial group is automatically a Kan complex. Like two years ago I read about this and they just gave some unexplained formula for how you can use the group structure to fill horns. Then today, as I was bored in a seminar, I figured out that it's nothing but a souped-up version of the Eckmann-Hilton argument saying that the composition of paths in a group is canonically homotopic to their pointwise product using the group structure. Why didn't they explain this in the book where I read it before??)
(Specifically, this was prompted by thinking about the fact that a simplicial group is automatically a Kan complex. Like two years ago I read about this and they just gave some unexplained formula for how you can use the group structure to fill horns. Then today, as I was bored in a seminar, I figured out that it's nothing but a souped-up version of the Eckmann-Hilton argument saying that the composition of paths in a group is canonically homotopic to their pointwise product using the group structure. Why didn't they explain this in the book where I read it before??)