generalize result to pointed categories

Author: ScriptRaccoon

database/data/005_implications/008_topos-theory-implications.sql

@@ -203,9 +203,9 @@ VALUES
 	FALSE
 ),
 (
-	'nno_additive_case',	
-	'["natural numbers object", "additive"]',
+	'nno_pointed_case',	
+	'["natural numbers object", "pointed"]',
 	'["trivial"]',
-	'Let $(N,z,s)$ be a natural numbers object in an additive category. The morphism $z : 0 \to N$ must be the zero morphism. The universal property applied to $A=1$ implies that $s : N \to N$ is an initial object in the category of endomorphisms. This exists, it is given by the identity $0 \to 0$. Therefore, $N = 0$. The general universal property now becomes: For all $f : A \to X$, $g : X \to X$ there is a unique $\Phi : A \to X$ such that $\Phi(a) = f(a)$ and $\Phi(a)=g(\Phi(a))$. Apply this to $g = 0$ to conclude $f = 0$ for all $f$.',
+	'Let $(N,z,s)$ be a natural numbers object in a category with a zero object, denoted $0$. The morphism $z : 0 \to N$ must be zero. The universal property applied to $A=1$ implies that $s : N \to N$ is an initial object in the category of endomorphisms. This exists, it is given by the identity $0 \to 0$. Therefore, $N = 0$. The general universal property now becomes: For all $f : A \to X$, $g : X \to X$ there is a unique $\Phi : A \to X$ such that $\Phi(a) = f(a)$ and $\Phi(a)=g(\Phi(a))$. Apply this to $g = 0$ to conclude $f = 0$.',
 	FALSE
 );