You were at lectures given by Hodge or by a PhD student of his?I did topology at undergrad level from Cambridge PhD student of W. V. D. Hodge. But not my forte.That is a very category theory like question.
But no, not at all. It's fascinating, like so many other things in maths and physics, but I have no talent for it/them.
You're in the realm of Riemann and Poincare who eat straws for breakfast.
Unfortunately, constructing Cauchy sequences on a torus is very difficult.
Not many people have a star named after them.