Definition 8.3:

The category ${\bf Top^2}$ of pairs has as its objects the class of all pairs of topological spaces $(X, A)$ where $X$ is a topological space and $A\subset X$. Given two pairs $(X, A)$ and $(Y, B)$ the set of morphisms between them is the class of all continuous functions $f : X \longrightarrow Y$ such that $f(A) \subset B$.