X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=advanced_topics%2Fmonads_in_category_theory.mdwn;h=29b6feb3e250ad195f8884215570afa5fe639ecf;hp=293c7e3129658647cc88dffafa63ab81d9de8ea0;hb=c4eb20ae862369e97cadef43183d0663f3eddd11;hpb=c7334eb4f97a0298dc5a1f37fc203c3587d24536;ds=sidebyside diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn index 293c7e31..29b6feb3 100644 --- a/advanced_topics/monads_in_category_theory.mdwn +++ b/advanced_topics/monads_in_category_theory.mdwn @@ -154,7 +154,7 @@ by naturalness of `η`, is: φ[C2] ∘ η[C2] ∘ G(f) = J(f) ∘ φ[C1] ∘ η[C1] -Hence, we can define `(φ -v- η)[x]` as: `φ[x] ∘ η[x]` and rely on it to satisfy the constraints for a natural transformation from `G` to `J`: +Hence, we can define `(φ -v- η)[\_]` as: `φ[\_] ∘ η[\_]` and rely on it to satisfy the constraints for a natural transformation from `G` to `J`:
``` 	(φ -v- η)[C2] ∘ G(f) = J(f) ∘ (φ -v- η)[C1]
@@ -173,7 +173,7 @@ I'll assert without proving that vertical composition is associative and has an

(φ -h- η)[C1]  =  L(η[C1]) ∘ ψ[G(C1)]
-					   =  ψ[H(C1)] ∘ K(η[C1])
+				  =  ψ[H(C1)] ∘ K(η[C1])

Horizontal composition is also associative, and has the same identity as vertical composition.
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