👉 Hilton Math, named after mathematician Arthur Hilton, is a powerful framework for proving the existence of certain mathematical structures, particularly in the context of category theory and higher category theory. At its core, it provides a method to construct objects and morphisms in a way that respects the compositionality and coherence of categories. The key idea is to use a sequence of small, controlled transformations, or "hilton maps," which are defined on objects and morphisms in a category. These maps ensure that the resulting structure satisfies specific coherence conditions, allowing one to build complex structures from simpler ones in a systematic and rigorous manner. This approach is especially useful for proving the existence of limits, colimits, and other categorical constructs, and it has found applications in various areas of mathematics, including algebraic topology, homotopy theory, and theoretical computer science.
