(ST : object ((A -> C)^op * (B -> C))) : Cat / !((A * B; PAB) : Cat). Proof. exists (Basics.Overture.fst ST / Basics.Overture.snd ST; P_comma _ _) (center _). exact (comma_category_projection (Basics.Overture.fst ST) (Basics.Overture.snd ST)). Defined.
Require Import Category.Core Functor.Core. Require Import Category.Prod Functor.Prod.Core. Require Import Category.Dual Functor.Dual. Require Import Functor.Composition.Core. Require Import InitialTerminalCategory.Core InitialTerminalCategory.Functors NatCategory. Require Import FunctorCategory.Core. Require Import Cat.Core. Require Import Functor.Paths. Import Comma.Core. Require Import Comma.InducedFunctors Comma.Projection. Require Import Types.Forall PathGroupoids HoTT.Tactics.