/-
Copyright (c) 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad

Short exact sequences
-/
import .quotient_group
open eq nat int susp pointed pmap sigma is_equiv equiv fiber algebra trunc trunc_index pi group
     is_trunc function sphere unit sum prod

structure is_short_exact {A B : Type} {C : Type*} (f : A → B) (g : B → C) :=
  (is_emb    : is_embedding f)
  (im_in_ker : Π(a:A), g (f a) = pt)
  (ker_in_im : Π(b:B), (g b = pt) → image f b)
  (is_surj   : is_surjective g)

structure is_short_exact_t {A B : Type} {C : Type*} (f : A → B) (g : B → C) :=
  (is_emb    : is_embedding f)
  (im_in_ker : Π(a:A), g (f a) = pt)
  (ker_in_im : Π(b:B), (g b = pt) → fiber f b)
  (is_surj   : is_split_surjective g)