(O : Modality) {F X Y : pType} (i : F ->* X) (f : X ->* Y) `{IsExact O _ _ _ i f} (x : X) (p : f x = point Y) : O (hfiber i x). Proof. rapply (O_functor O (A:=hfiber (cxfib cx_isexact) (x; p))). - intros [z q]. exact (z; ap pr1 q). - apply center, conn_map_isexact. Defined.
Require Import Basics Types. Require Import SuccessorStructure. Require Import WildCat. Require Import Pointed. Require Import Modalities.Identity Modalities.Descent. Require Import Truncations. Require Import HFiber. Require Import ObjectClassifier.