`{Funext} A B (S : Pseudofunctor A) (T : Pseudofunctor B) `{forall a b, IsHSet (Functor (S a) (T b))} : PreCategory := @Build_PreCategory (@object _ _ _ S T) (@morphism _ _ _ S T) (@identity _ _ _ S T) (@compose _ _ _ S T) (@associativity _ _ _ S T) (@left_identity _ _ _ S T) (@right_identity _ _ _ S T) _.
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.