范畴化是把集合理论推广为范畴理论的一个过程，其把等号推广为同构。范畴化把简单的对象变得复杂但包含丰富的信息，比如，把整数变为向量空间，使得向量空间的维数等于原来的整数。. 现在已经实现了海森堡代数的范畴化，我们利用玻色-费米对应，将把费米子提升为一个同伦范畴中的复形，并构造范畴化的玻色-费米对应，然后我们想找出它们在可积系统中的应用。

Categorification is a process in which sets are replaced by categories and equalities by isomorphisms. It changes a simpler object to a more sophisticated but richer one, such as, changes a integer number to a vector space whose dimension equals this number. . The Heisenberg algebra has been categorified now. By Boson-Fermion correspondence, we will lift Fermions to complexes in a homotopy category, and construct the categorified Boson-Fermion correspondence, then we want to find their applications in integrable system.