Definition is_left_adjoint_slice_dom {C : category} (BP : BinProducts C) (x : C) : is_left_adjoint (slice_dom x). Proof. use left_adjoint_from_partial. - exact (λ z, pr_cod_fib BP x z). - exact (λ z, BinProductPr2 _ (BP x z)). - intros z yf g. use iscontraprop1. + apply is_left_adjoint_slice_dom_unique. + simple refine (_ ,, _). * exact (is_left_adjoint_slice_dom_mor BP yf g). * apply is_left_adjoint_slice_dom_comm. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.Limits.BinProducts.