# Differences

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 a_triangle_limit [2016/05/21 15:28]nikolaj created a_triangle_limit [2016/05/21 18:25] (current)nikolaj 2016/05/21 18:25 nikolaj 2016/05/21 15:28 nikolaj created 2016/05/21 18:25 nikolaj 2016/05/21 15:28 nikolaj created Line 25: Line 25: {{ 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 $e=\{x\in a\ |\ f(x)=g(x)\}$.