First, that's not what your link says. (See, e.g., the comments to the first answer.) Second, I find that claim highly dubious. To do metamathematics and talk

First, that's not what your link says. (See, e.g., the comments to the first answer.) Second, I find that claim highly dubious. To do metamathematics and talk about the relative strength of various axiomatic systems, you need to talk about large cardinals. So that, at least to me, seems like a good argument that set theory is foundational to mathematics in a way that category theory is not, since the latter has no non-eliminable place in the (study of) contemporary foundations of mathematics.