{H K : Group} : H $-> (grp_prod H K) := grp_prod_corec grp_homo_id grp_homo_const. Global Instance isembedding_grp_prod_inl {H K : Group} : IsEmbedding (@ H K). Proof. apply isembedding_isinj_hset. intros h0 h1 p; cbn in p. exact (fst ((equiv_path_prod _ _)^-1 p)). Defined.
Require Import Basics Types HProp HFiber HSet. Require Import Homotopy.IdentitySystems. Require Import (notations) Classes.interfaces.canonical_names. Require Import Pointed.Core. Require Import WildCat. Require Import Spaces.Nat.Core Spaces.Int. Require Import Truncations.Core.