1 files changed, 6 insertions, 6 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 41aef99..f95c068 100644
--- a/provider/posts/simmons-intro-to-cat-t/1.1.md
+++ b/provider/posts/simmons-intro-to-cat-t/1.1.md
@@ -10,8 +10,8 @@ Sets and functions do form a category $\ca{Set}$.
 <div class="proof">
 The objects of $\ca{Set}$ are sets and its arrows are functions.
 
-For any set $A$ we construct $id_A$ by restricting $id$ to $A$:
-$$id_A = id \upharpoonright A$$
+For any set $A$ we construct \idarr{A} by restricting \id to $A$:
+$$\idarr{A} = \id \upharpoonright A$$
 
 $\circ$ is indeed associative.
 </div>
@@ -21,9 +21,9 @@ $\circ$ is indeed associative.
 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 $\leq: a \to b$ for every pair of objects $(a, b)$ iff $a \leq b$.
+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 $a \leq b$.
 
-Reflexivity ($a \leq a$) and transitivity ($a \leq b \land b \leq c \implies a \leq c$) provide a construction for $id_a$ and $\circ$, respectively.
+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>
 
@@ -31,8 +31,8 @@ Reflexivity ($a \leq a$) and transitivity ($a \leq b \land b \leq c \implies a \
 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 $\cdot b : a \to a \cdot b$.
+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 existence of an identity element and associativity, as required by the monoid structure, immediately provide us with a construction for $id$ and associativity of $\circ$.
+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>
 </div>