# Commutative diagrams

From Why start at x, y, z

In category theory, reading commutative diagrams requires an understanding of which variables are bound and which are free. Some authors choose to annotate their diagrams with universal quantifiers like \( \forall x,y,z \) to indicate the set of free variables, implying the rest are bound.

When such annotations are not included, the diagram alone is not precise enough to decode the intended logical statement. To read a commutative diagram, we must infer the bound and free variables from context.