fact: Definition lax_arrow_category : PreCategory := @lax_comma_category _ cat cat (Pseudofunctor.Identity.identity P) (Pseudofunctor.Identity.identity P) (fun C D => HF C.2 D.2).
imports: Functor.Core Category.Dual InitialTerminalCategory.Core InitialTerminalCategory.Pseudofunctors Cat.Core Category.Strict NaturalTransformation.Paths Pseudofunctor.Core