more concise arrows & exercise envs

1 files changed, 5 insertions, 5 deletions

diff --git a/provider/posts/simmons-intro-to-cat-t/1.1.md b/provider/posts/simmons-intro-to-cat-t/1.1.md
index 6c69c62..1b6c16d 100644
--- a/provider/posts/simmons-intro-to-cat-t/1.1.md
+++ b/provider/posts/simmons-intro-to-cat-t/1.1.md
@@ -4,7 +4,7 @@ published: 2016-01-29
 tags: Category Theory
 ---
 
-<div class="corollary">
+<div class="exercise">
 Sets and functions do form a category $\ca{Set}$.
 
 <div class="proof">
@@ -16,21 +16,21 @@ $\circ$ is indeed associative.
 </div>
 </div>
 
-<div class="corollary">
+<div class="exercise">
 Each [poset](https://en.wikipedia.org/wiki/Partially_ordered_set) is a category.
 
 <div class="proof">
-The objects of each poset are its elements and we construct an arrow $\begin{tikzcd} a \arrow[r, "\leq"] & b \end{tikzcd}$ for every pair of objects $(a, b)$ iff $a \leq b$.
+The objects of each poset are its elements and we construct an arrow $\arr{a}{\leq}{b}$ for every pair of objects $(a, b)$ iff $a \leq b$.
 
 Reflexivity ($a \leq a$) and transitivity ($a \leq b \land b \leq c \implies a \leq c$) provide a construction for $\idarr{a}$ and $\circ$, respectively.
 </div>
 </div>
 
-<div class="corollary">
+<div class="exercise">
 Each [monoid](https://en.wikipedia.org/wiki/Monoid) is a category.
 
 <div class="proof">
-The objects of each monoid are its elements and we construct for every pair of elements $(a, b)$ an arrow $\begin{tikzcd} a \arrow[r, "\cdot b"] & a \cdot b \end{tikzcd}$.
+The objects of each monoid are its elements and we construct for every pair of elements $(a, b)$ an arrow $\arr{a}{\cdot b}{a \cdot b}$.
 
 The existence of an identity element and associativity, as required by the monoid structure, immediately provide us with a construction for $\id$ and associativity of $\circ$.
 </div>