Definition connected_groupoid_to_connected_category {G : groupoid} (H : connected_groupoid G) : connected_category G. Proof. use make_connected_category. - exact (ob_of_connected_groupoid H). - exact (λ x y, x -[ mor_of_connected_groupoid H x y ]-> 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.