`{Funext} A B (S : Pseudofunctor A) (T : Pseudofunctor B) `{forall a b, IsHSet (Functor (S a) (T b))} : PreCategory := (lax_comma_category S T)^op. Global Instance isstrict_lax_comma_category `{Funext} A B (S : Pseudofunctor A) (T : Pseudofunctor B) `{IsStrictCategory A, IsStrictCategory B} `{forall a b, IsHSet (Functor (S a) (T b))} : IsStrictCategory (@lax_comma_category _ A B S T _). Proof. typeclasses eauto. Qed.
Require Import Functor.Core. Require Import Category.Dual. Require Import InitialTerminalCategory.Core InitialTerminalCategory.Pseudofunctors. Require Import Cat.Core. Require Import Category.Strict. Require Import NaturalTransformation.Paths. Require Import Pseudofunctor.Core. Import Functor.Identity.FunctorIdentityNotations. Import Pseudofunctor.Identity.PseudofunctorIdentityNotations. Import LaxComma.CoreLaws.LaxCommaCategory.