Category Theory is a subfield of Mathematics studying mathematical structures and their conservation through various transformation. It emerged in the study of algebraic topology, then went on to apply to most parts of mathematics.
Despite some work on applied category theory, it's usefulness for problem solving (especially in topics close to LW, such as Rationality and AI Safety) is still controversial. One possible explanation is that category theory usually comes after the results, to structure them and find the links with previous results in other fields.