# Category A category is **a collection of *objects* with certain properties (which are a part of the category's definition) that are linked by *arrows* called [[Morphism]]-s**. This implies that for every object there must exist an arrow that links the object to itself. ![[Category Theory - Wikipedia#^qp7cz1]] **An example of a category in algebra is the category of sets, whose objects are sets, and whose arrows are [[Function (in Algebra)|functions]].**