Definition connected_category_to_connected_groupoid {G : groupoid} (H : connected_category G) : connected_groupoid G. Proof. use make_connected_groupoid. - exact (ob_of_connected_category H). - exact (λ x y, zig_zag_in_grpd_to_mor (zig_zag_of_connected_category H x y)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.CategoryTheory.ZigZag.