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a_triangle_limit [2016/05/21 15:28]
nikolaj created
a_triangle_limit [2016/05/21 18:25] (current)
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 {{ category_theory_equalizer_diagram.png?​X200}} {{ category_theory_equalizer_diagram.png?​X200}}
-If $h$ is an isomorphism $h:c\simeq a$, then we're left with a two-parallel-arrows situation. ​+If $h$ is an isomorphism $h:c\simeq a$, then we can replace $c$ by $a$ and we're left with a pullback. This can also be viewed as a two-parallel-arrows situation, and it is called the [[equalizer]].
 In ${\bf{Set}}$,​ if $h$ is an iso, the object is $e=\{x\in a\ |\ f(x)=g(x)\}$. In ${\bf{Set}}$,​ if $h$ is an iso, the object is $e=\{x\in a\ |\ f(x)=g(x)\}$.
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