Don't think anybody told me that, but I do believe it to be the case

Why?

Category theory is equivalent to type theory.

It's probably more accurate to say that they are complementary rather than equivalent.

- Category theory emphasizes morphisms and composition

- Type theory emphasizes terms and computation

There are important correspondences between them (like the Curry-Howard-Lambek correspondence), but they have different strengths and different ways of expressing concepts.

Sorry, I couldn't resist the temptation of being a pedantic formalist.