Literally. An abstract category is an abstract abstraction. That's the realm of metaphysics.
Ayn Rand was a student of the classic Greek philosophy, nothing wrong with her.
Ayn Rand was a student of the classic Greek philosophy, nothing wrong with her.
However, her status as an intellectual heir of Aristotle is highly debatable. She's as much a disciple of Nietzsche as anyone.
Meanwhile, metaphysics is a subject that stems directly from Greek philosophy: specifically the subjects addressed in Aristotle's work Metaphysics (literally "the book that came after Physics"). Spinoza's theory of monism is itself a metaphysical theory in this sense.
Perhaps by metaphysics, you mean to certain metaphysical theories, such as the Idealism of the 18th century?
edit: missing punctuation
> Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world that encompasses it. Metaphysics attempts to answer two basic questions in the broadest possible terms:
> Ultimately, what is there? What is it like?
Does category theory have anything to do with that? No.
> Does category theory have anything to do with that? No.
I could argue that category theory is claiming to answer those questions for mathematics. (So is the axiomatization based on set theory.)