Why Higher Category Theory in Physics? - Comments

[stevendaryl]

Remarkably, homotopy theory is a "smaller theory": it arises from classical theory by removing axioms from classical logic. This is the fantastic insight of homotopy type theory.

Well, larger versus smaller or simpler versus more complex depends on how you measure things. You can understand classical mathematics as being a simplification of constructive mathematics, in which you toss out distinctions. (such as the distinction between a proof of $A$ and a proof of $\neg \neg A$)