2017-03-02 22:06:13 +00:00
|
|
|
/-
|
|
|
|
|
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)
|
2017-03-02 22:08:00 +00:00
|
|
|
(is_surj : is_split_surjective g)
|
