proposition: Proposition composition_preserves_chosen_terminal_eq {C₁ C₂ C₃ : category} {F : C₁ ⟶ C₂} {G : C₂ ⟶ C₃} {T₁ : Terminal C₁} {T₂ : Terminal C₂} {T₃ : Terminal C₃} (HF : preserves_chosen_terminal_eq F T₁ T₂) (HG : preserves_chosen_terminal_eq G T₂ T₃) : preserves_chosen_terminal_eq (F ∙ G) T₁ T₃.
proof: Proof. revert HF. use factor_through_squash. { apply propproperty. } intro p. revert HG. use factor_through_squash. { apply propproperty. } intro q. cbn. apply hinhpr. rewrite p, q. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Adjunctions.Core