Differences
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categories [2016/11/26 22:28] jipsen |
categories [2016/11/27 09:54] (current) jipsen |
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| $\langle C,\circ\rangle$ is a (large) [[partial semigroup]] | $\langle C,\circ\rangle$ is a (large) [[partial semigroup]] | ||
| + | |||
| + | dom amd cod are total unary operations on $C$ such that | ||
| $\text{dom}(x)$ is a left unit: $\text{dom}(x)\circ x=x$ | $\text{dom}(x)$ is a left unit: $\text{dom}(x)\circ x=x$ | ||
| $\text{cod}(x)$ is a right unit: $x\circ\text{cod}(x)=x$ | $\text{cod}(x)$ is a right unit: $x\circ\text{cod}(x)=x$ | ||
| - | |||
| - | $\text{dom}(\text{dom}(x))=\text{dom}(x)=\text{cod}(\text{dom}(x))$ | ||
| - | |||
| - | $\text{cod}(\text{cod}(x))=\text{cod}(x)=\text{dom}(\text{cod}(x))$ | ||
| if $x\circ y$ exists then $\text{dom}(x\circ y)=\text{dom}(x)$ and $\text{cod}(x\circ y)=\text{cod}(y)$ | if $x\circ y$ exists then $\text{dom}(x\circ y)=\text{dom}(x)$ and $\text{cod}(x\circ y)=\text{cod}(y)$ | ||
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| ====Basic results==== | ====Basic results==== | ||
| + | $\text{dom}(\text{dom}(x))=\text{dom}(x)=\text{cod}(\text{dom}(x))$ | ||
| + | |||
| + | $\text{cod}(\text{cod}(x))=\text{cod}(x)=\text{dom}(\text{cod}(x))$ | ||
| ====Properties==== | ====Properties==== | ||
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