# Differences

This shows you the differences between two versions of the page.

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