`{Funext} (A B B' : pType) (f : psusp A ->* B) (g : B ->* B') : loop_susp_adjoint A B' (g o* f) ==* fmap loops g o* loop_susp_adjoint A B f. Proof. pointed_reduce. srefine (Build_pHomotopy _ _). - intros a. simpl. refine (_ @ (concat_1p _)^). refine (_ @ (concat_p1 _)^). rewrite !transport_sigma. simpl. rewrite !(transport_arrow_fromconst (B := A)). rewrite !transport_paths_Fr. rewrite !ap_V, !ap_pr1_path_basedpaths. Fail rewrite ap_pp, !(ap_compose f g), ap_V. Fail reflexivity. admit. - cbn. Fail reflexivity. Abort. >> *) End Book_Loop_Susp_Adjunction.
Require Import Basics. Require Import Types. Require Import Pointed.Core. Require Import Pointed.Loops. Require Import Pointed.pTrunc. Require Import Pointed.pEquiv. Require Import Homotopy.Suspension. Require Import Homotopy.Freudenthal. Require Import Truncations. Require Import WildCat.