Aristotle wrote near the very beginning of the golden age of Greek mathematics. He criticized the mathematics of his day (arithmetic and geometry) as being useful but insufficiently abstract, which was a very valid point at the time. In particular, it did not offer much support for showing the intelligibility of becoming, which was his main goal in the Physics. He also took a strong stand against Pythagorean superstition, which at the time was hard to separate from enthusiasm for mathematics.

We do not know how Aristotle would have responded to category theory or homotopy type theory, or even algebra or calculus. But given the nature of his criticism, it seems extremely questionable to simply assume he would not have welcomed such advances.