Diagonal functor
In category theory, a branch of mathematics, the diagonal functor C → C × C {\displaystyle {\mathcal {C}}\rightarrow {\mathcal {C}}\times {\mathcal {C}}} is given by Δ ( a ) = ⟨ a , a ⟩ {\displaystyle \Delta (a)=\langle a,a\rangle } , which maps objects as well as morphisms. This functor can be employed to give a succinct alternate description of the product of objects within the category C {\displaystyle {\mathcal {C}}} : a product a × b {\displaystyle a\times b} is a universal arrow from Δ {\displaystyle \Delta } to ⟨ a , b ⟩ {\displaystyle \langle a,b\rangle } .