projects
/
coq-categories.git
/ commitdiff
commit
grep
author
committer
pickaxe
?
search:
re
summary
|
shortlog
|
log
|
commit
| commitdiff |
tree
raw
|
patch
|
inline
| side by side (parent:
0ecd73c
)
add inverse form of ni_commutes
master
author
Adam Megacz
<megacz@cs.berkeley.edu>
Sun, 24 Apr 2011 07:00:24 +0000
(
00:00
-0700)
committer
Adam Megacz
<megacz@cs.berkeley.edu>
Sun, 24 Apr 2011 07:00:24 +0000
(
00:00
-0700)
src/NaturalIsomorphisms_ch7_5.v
patch
|
blob
|
history
diff --git
a/src/NaturalIsomorphisms_ch7_5.v
b/src/NaturalIsomorphisms_ch7_5.v
index
c62ba15
..
ce97ce6
100644
(file)
--- a/
src/NaturalIsomorphisms_ch7_5.v
+++ b/
src/NaturalIsomorphisms_ch7_5.v
@@
-19,6
+19,17
@@
Implicit Arguments ni_commutes [Ob Hom Ob0 Hom0 C1 C2 Fobj1 Fobj2 F1 F2 A B].
Coercion ni_iso : NaturalIsomorphism >-> Funclass.
Notation "F <~~~> G" := (@NaturalIsomorphism _ _ _ _ _ _ _ _ F G) : category_scope.
Coercion ni_iso : NaturalIsomorphism >-> Funclass.
Notation "F <~~~> G" := (@NaturalIsomorphism _ _ _ _ _ _ _ _ F G) : category_scope.
+(* same as ni_commutes, but phrased in terms of inverses *)
+Lemma ni_commutes' `(ni:NaturalIsomorphism) : forall `(f:A~>B), F2 \ f >>> #(ni_iso ni B)⁻¹ ~~ #(ni_iso ni A)⁻¹ >>> F1 \ f.
+ intros.
+ apply iso_shift_right'.
+ setoid_rewrite <- associativity.
+ symmetry.
+ apply iso_shift_left'.
+ symmetry.
+ apply ni_commutes.
+ Qed.
+
(* FIXME: Lemma 7.11: natural isos are natural transformations in which every morphism is an iso *)
(* every natural iso is invertible, and that inverse is also a natural iso *)
(* FIXME: Lemma 7.11: natural isos are natural transformations in which every morphism is an iso *)
(* every natural iso is invertible, and that inverse is also a natural iso *)