minor corrections

1 files changed, 4 insertions, 4 deletions

diff --git a/provider/posts/simmons-intro-to-cat-t/1.2.md b/provider/posts/simmons-intro-to-cat-t/1.2.md
index e180c6d..faaf429 100644
--- a/provider/posts/simmons-intro-to-cat-t/1.2.md
+++ b/provider/posts/simmons-intro-to-cat-t/1.2.md
@@ -14,7 +14,7 @@ Let $\ca{Pno}$ be the category of objects $(A, \alpha, a)$ where $A$ is a set, $
         $\id$ on $A$ is indeed a function which preserves the structure ($\id \circ \alpha = \alpha = \alpha \circ \id$, $\id(a) = a$) and thus a morphism
         </div>
         
-     2. There exists a partial binary operation $\circ$ on the arrows of $\ca{Pno}$
+     2. There exists an associative partial binary operation $\circ$ on the arrows of $\ca{Pno}$
         <div class="proof">
         Given three objects $(A, \alpha, a), (B, \beta, b), (C, \gamma, c)$ and two functions $g: A \to B$ and $f: B \to C$ the function $f \circ g: A \to C$ is an arrow in $\ca{Pno}$, that is to say, it preserves structure:
         $$(f \circ g) \circ \alpha = f \circ \beta \circ g = \gamma \circ (f \circ g)$$
@@ -62,7 +62,7 @@ Show that such objects and morphisms form a category $\ca{SetD}$
     $\id$ on $A$ is indeed a function which respects the distinguished subset ($\forall \alpha \in a \ldotp \id(\alpha) \in a$) and thus a morphism
     </div>
     
- 2. There exists a partial binary operation $\circ$ on the arrows of $\ca{SetD}$
+ 2. There exists an associative partial binary operation $\circ$ on the arrows of $\ca{SetD}$
     <div class="proof">
     Given three objects $(A, a), (B, b), (C, c)$ and two functions $g: A \to B$ and $f: B \to C$ the function $f \circ g: A \to C$ is an arrow in $\ca{SetD}$, that is to say, $\forall \alpha \in a$:
     $$(f \circ g)(\alpha) = f(b) = c$$
@@ -83,7 +83,7 @@ We call the category comprised of such objects and arrows $\ca{RelH}$.
 
     $\id$ on $A$ is indeed a function which respects the binary relation ($\forall a \odot a^\prime \ldotp \id(a) \odot \id(a^\prime)$) and thus a morphism
     
- 2. There exists a partial binary operation $\circ$ on the arrows of $\ca{RelH}$
+ 2. There exists an associative partial binary operation $\circ$ on the arrows of $\ca{RelH}$
 
     Given three objects $(A, \odot), (B, \oplus), (C, \otimes)$ and two functions $g: A \to B$ and $f: B \to C$ the function $f \circ g: A \to C$ is an arrow in $\ca{RelH}$, that is to say, $\forall a \odot a^\prime$:
     $$a \odot a^\prime \implies g(a) \oplus g(a^\prime) \implies (g \circ f)(a) \otimes (g \circ f)(a^\prime)$$
@@ -98,7 +98,7 @@ Topological spaces $(S, \mathcal{O}_S)$, where $S$ is a Set and $\mathcal{O}_S \
     $\id$ on $S$ is indeed a continuous map and thus a morphism
     </div>
     
- 2. There exists a partial binary operation $\circ$ on the arrows of $\ca{Top}$
+ 2. There exists an associative partial binary operation $\circ$ on the arrows of $\ca{Top}$
     <div class="proof">
     Given three spaces $(S, \mathcal{O}_S), (T, \mathcal{O}_T), (U, \mathcal{O}_U)$ and two continuous maps $g : S \to T$ and $f : T \to U$ the map $f \circ g : S \to U$ is an arrow in $\ca{Top}$, that is to say, it is contiuous:
     $$V \in \mathcal{O}_U \implies g^\leftarrow(V) \in \mathcal{O}_T \implies (f \circ g)^\leftarrow(V) \in \mathcal{O}_S$$