Definition weakly_terminal_to_connected {C : category} (c : C) (fs : ∏ (w : C), w --> c) : connected_category C. Proof. use make_connected_category. - exact c. - exact (λ x y, x -[ fs x ]-> c <-[ fs 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.