Definition leftwhiskering_dispfunctor {A B C : category} {F : bifunctor A B C} {DA : disp_cat A} {DB : disp_cat B} {DC : disp_cat C} (DF : disp_bifunctor_data F DA DB DC) (dbli : disp_bifunctor_leftidax DF) (dblc : disp_bifunctor_leftcompax DF) : ∏ (x : A) (xx : DA x), disp_functor (leftwhiskering_functor F x) DB DC. Proof. intros x xx. use tpair. - use tpair. + intros y yy. exact (xx ⊗⊗_{DF} yy). + intros y1 y2 yy1 yy2 g gg. exact (xx ⊗⊗^{DF}_{l} gg). - use tpair. + intros y yy. exact (dbli x y xx yy). + intros y1 y2 y3 yy1 yy2 yy3 g1 g2 gg1 gg2. cbn. exact (dblc x y1 y2 y3 g1 g2 xx yy1 yy2 yy3 gg1 gg2). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Core.Isos. Import BifunctorNotations. Import DisplayedBifunctorNotations.