Functor ((A -> C)^op * (B -> C)) (Cat / !((A * B; PAB) : Cat)) := Build_Functor ((A -> C)^op * (B -> C)) (Cat / !((A * B; PAB) : Cat)) comma_category_projection_functor_object_of comma_category_projection_functor_morphism_of comma_category_projection_functor_composition_of comma_category_projection_functor_identity_of.
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.