As grand-nibling comment suggests, it's primarily about vocabulary and definitions, but also how objects can be put together to form new objects. In combination

As grand-nibling comment suggests, it's primarily about vocabulary and definitions, but also how objects can be put together to form new objects. In combination, we end up with "universal properties", behaviors of objects which are the same in many different contexts. If you want to get some surface-level mind-blown experiences, then there are some cool pages out there, in addition to the papers I already linked, which have great diagrams. [0] shows a periodic table which relates categories to truth values and sets, which is helpful for understanding what folks mean by "category theory is just as good as set theory for foundational work". More mind-blowingly, category theory is "formally formal", which means that we can use category theory to formalize its own concepts. This leads to n-category theory. Because of this, we have tables like [1] which relate category theory's own building blocks to type theory and logic. Category theory was originally the study of natural transformations. Any time that you find enough data to define a natural transformation, then that's interesting; the component categories are then also interesting objects of study. That's still what motivates its presence in physics. There are at least two other perspectives though, a logical perspective (a category is a deductive system for a formal logic) and a spatial perspective (a category is a topological space), and they're both rich as well. But the richest perspective is going to come after you've explored all three. [0] https://ncatlab.org/nlab/show/periodic+table https://ncatlab.org/nlab/show/periodic+table [1] https://ncatlab.org/nlab/show/computational+trinitarianism https://ncatlab.org/nlab/show/computational+trinitarianism