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=3e34f85b8e2841bacb7675190bd3e30ed77b425d;hb=c4eb20ae862369e97cadef43183d0663f3eddd11;hpb=7026bf51a9211af0586d30d49b61ed187f897a79
diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index 3e34f85b..29b6feb3 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -121,13 +121,13 @@ Consider four categories B, C, D, and E. Let `F` be
- B -+ +--- C --+ +---- D -----+ +-- E --
| | | | | |
- F: -----→ G: -----→ K: -----→
- | | | | | η | | | ψ
+ F: ------> G: ------> K: ------>
+ | | | | | η | | | ψ
| | | | v | | v
- | | H: -----→ L: -----→
- | | | | | φ | |
+ | | H: ------> L: ------>
+ | | | | | φ | |
| | | | v | |
- | | J: -----→ | |
+ | | J: ------> | |
-----+ +--------+ +------------+ +-------
@@ -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.