I think you're misunderstanding what anarchy is supposed to look like. How does one capitalize in an anarchist society divorced from capitalism? As in, what do

I think you're misunderstanding what anarchy is supposed to look like. How does one capitalize in an anarchist society divorced from capitalism? As in, what does capital mean? What does it mean to profit? How can one "outcompete" a "socialist firm"? When there is no money or private property, every firm belongs to everyone who wants it. Why is a state necessary to punish hierarchies? Presumably in an anarchist world, people have learned to distrust and dislike hierarchies on principle, refuse to partake in it and join together to punish those who do.