fact: Definition comma_category_projection : Functor (S / T) (A * B) := Build_Functor (S / T) (A * B) (fun abf => (CommaCategory.a abf, CommaCategory.b abf)%core) (fun _ _ m => (CommaCategory.g m, CommaCategory.h m)%core) (fun _ _ _ _ _ => idpath) (fun _ => idpath).
imports: Category.Core Functor.Core Category.Prod Functor.Prod.Core Functor.Composition.Core Functor.Identity InitialTerminalCategory.Functors Types.Prod