That's not an application of category theory. The important theorem here is that the fundamental group is a functor, plus computations of the fundamental group of the disc and the circle. But that's a theorem from topology, not a theorem from category theory. Category theory is merely used as a language, to give the proof a structure.
By that I don't want to say category theory is useless. But regarding the video it's neither necessary, nor an application of category theory.
That's not an application of category theory. The important theorem here is that the fundamental group is a functor, plus computations of the fundamental group of the disc and the circle. But that's a theorem from topology, not a theorem from category theory. Category theory is merely used as a language, to give the proof a structure.
By that I don't want to say category theory is useless. But regarding the video it's neither necessary, nor an application of category theory.