X-Git-Url: http://git.megacz.com/?p=coq-categories.git;a=blobdiff_plain;f=src%2FCoherence_ch7_8.v;fp=src%2FCoherence_ch7_8.v;h=26652552b3c114ec7cef69f666e8a2a843bf7ffb;hp=d683b9069129650bacda895baa7ea5c613fe071e;hb=1dd1bee2b13b43812ebbc078bdbf774886392886;hpb=e928451c4c45cdbdd975bbfb229e8cc2616b8194 diff --git a/src/Coherence_ch7_8.v b/src/Coherence_ch7_8.v index d683b90..2665255 100644 --- a/src/Coherence_ch7_8.v +++ b/src/Coherence_ch7_8.v @@ -16,14 +16,14 @@ Section Coherence. {bobj:C->C->C} (first : forall a b c:C, (a~~{C}~~>b) -> ((bobj a c)~~{C}~~>(bobj b c))) (second : forall a b c:C, (a~~{C}~~>b) -> ((bobj c a)~~{C}~~>(bobj c b))) - (assoc : forall a b c:C, (bobj (bobj a b) c) ~~{C}~~> (bobj a (bobj b c))). + (assoc : forall a b c:C, (bobj a (bobj b c)) ~~{C}~~> (bobj (bobj a b) c)). Record Pentagon := - { pentagon : forall a b c d, (first _ _ d (assoc a b c )) >>> - (assoc a _ d ) >>> - (second _ _ a (assoc b c d )) - ~~ (assoc _ c d ) >>> - (assoc a b _ ) + { pentagon : forall a b c d, (assoc a _ _ ) >>> + (assoc _ _ _ ) ~~ + (second _ _ a (assoc b c d )) >>> + (assoc _ _ _ ) >>> + (first _ _ _ (assoc a b _ )) }. Context {I:C} @@ -31,7 +31,7 @@ Section Coherence. (cancelr : forall a :C, (bobj a I) ~~{C}~~> a). Record Triangle := - { triangle : forall a b, (first _ _ b (cancelr a)) ~~ (assoc a I b) >>> (second _ _ a (cancell b)) + { triangle : forall a b, (assoc a I b) >>> (first _ _ b (cancelr a)) ~~ (second _ _ a (cancell b)) (* * This is taken as an axiom in Mac Lane, Categories for the Working