 Pullback (category theory)

The pullback of $X\to Z\leftarrow Y$ is a universal commutative square with an object mapping to $X$ and $Y$. In the Category of sets, it is the set of pairs with equal images in $Z$.

In category theory, a **pullback** is a way of constructing a new object (or diagram) that represents the idea of "pulling back" information from two morphisms through a common codomain. It can be thought of as a limit in the category of sets (or in any category where limits exist), and it captures how two morphisms can be jointly represented.