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functor [2016/04/09 14:21] nikolaj |
functor [2016/04/09 14:22] nikolaj |
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| === Discussion === | === Discussion === | ||
| A function $f:C\to D$ maps a set of things $C=\{a,b,c,\dots\}$ into another set of things $D=\{f(a),f(b),f(c),\dots,\dots\}$ (remark: some of the listed elements in $D$ might be equal and $D$ might also be larger as the range of $f$). | A function $f:C\to D$ maps a set of things $C=\{a,b,c,\dots\}$ into another set of things $D=\{f(a),f(b),f(c),\dots,\dots\}$ (remark: some of the listed elements in $D$ might be equal and $D$ might also be larger as the range of $f$). | ||
| - | Let write $C$ as $\{1_a,1_b,1_c,\dots\}$, which is just a formal relabeling. | + | Let's write $C$ as $\{1_a,1_b,1_c,\dots\}$, which is just a formal relabeling. |
| A category ${\bf C}$ is richer than a set $C$: | A category ${\bf C}$ is richer than a set $C$: | ||
