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Merge branch 'master' of https://github.com/cmu-phil/Spectral

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Egbert Rijke 2017-03-02 17:11:26 -05:00
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/-
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)