A product of X and Y is an object, denoted X × Y, together with morphisms pX : X × Y → X and pY : X × Y → Y such that for all objects C together with morphisms f : C → X and g : C → Y, t...A product of X and Y is an object, denoted X × Y, together with morphisms pX : X × Y → X and pY : X × Y → Y such that for all objects C together with morphisms f : C → X and g : C → Y, there exists a unique morphism C → X × Y, denoted ⟨f , g⟩, for which the following diagram commutes: A morphism of cones (C, c∗) → (C′, c∗′) is a morphism a : C → C′ in C such that for all j ∈ J we have cj = a ; c′j.
