How does the concept of homotopy type theory (HoTT) enable the unification of homotopy theory and higher category theory in mathematical foundations?

What the electroweak unification achieved — Glashow, Salam, and Weinberg showed EM and weak force are one

Unified electroweak theory: EM and weak force as one interaction

What the Y combinator does: enables recursion in languages without named functions

The Y combinator enables recursive function definitions in lambda calculus and similar functional languages

What the underdetermination of theory by data means — evidence is always compatible with multiple theories

Underdetermination implies that evidence does not uniquely determine a single theory

What the Yoneda lemma says: an object is determined by its relationships to all other objects

Yoneda lemma: Morphisms from an object to all others uniquely determine the object

What a sigma-algebra is: a collection of sets closed under complement and countable union

A sigma-algebra is a set of subsets closed under complementation and countable unions

What string theory proposes — fundamental objects are 1D strings vibrating in 10 or 11 dimensions

String theory posits fundamental objects as 1D strings in 10 or 11 dimensions