Diagonal morphism
In category theory, a branch of mathematics, for every object A {\displaystyle A} in every category C {\displaystyle {\mathcal {C}}} where the product A × A {\displaystyle A\times A} exists, there exists the diagonal morphism δ A : A → A × A {\displaystyle \delta _{A}:A\rightarrow A\times A} satisfying π k ∘ δ A = id A {\displaystyle \pi _{k}\circ \delta _{A}=\operatorname {id} _{A}} for k ∈ { 1 , 2 } , {\displaystyle k\in \{1,2\},} where π k {\displaystyle \pi _{k}} is the canonical projection morphism to the k {\displaystyle k} -th component. The existence of this morphism is a consequence of the universal property that characterizes the product (up to isomorphism).