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equalizer_._category_theory [2016/05/19 19:53] nikolaj |
equalizer_._category_theory [2016/05/21 18:26] nikolaj |
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| + | {{ category_theory_equalizer_diagram.png?X200}} | ||
| === Examples === | === Examples === | ||
| - | In ${\bf{Set}}$, if $f,g:A\to B$, then their equalizer $E$ is the set $\{a\in A\ |\ f(a)=g(a)\}$ and $e:E\to A$ is the obvious injection. | + | In ${\bf{Set}}$, if $f,g:A\to B$, then their equalizer is the set |
| + | $E=\{a\in A\ |\ f(a)=g(a)\}$ | ||
| + | |||
| + | and $e:E\to A$ is the obvious injection. | ||
| + | |||
| + | Remark: In the image, $e=E$ and $i=e$. | ||
| === Reference === | === Reference === | ||
| nLab: [[http://ncatlab.org/nlab/show/equalizer|Equalizer]] | nLab: [[http://ncatlab.org/nlab/show/equalizer|Equalizer]] | ||
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| === Context === | === Context === | ||
| [[Functor]] | [[Functor]] | ||
| - | === Refinement of === | + | === Subset of === |
| - | [[Limit . category theory]] | + | [[A triangle limit]] |
