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Update databases/catdat/data/003_category-property-assignments/CompHaus.sql
Co-authored-by: Script Raccoon <scriptraccoon@gmail.com>
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databases/catdat/data/003_category-property-assignments/CompHaus.sql

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'CompHaus',
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'cogenerator',
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TRUE,
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'The unit interval $[0, 1]$ is a cogenerator: Suppose we have $f, g : X \to Y$ with $f \ne g$. Choose $x\in X$ such that $f(x) \ne g(x)$. Then by Urysohn''s lemma, there is a function $h : Y \to [0, 1]$ such that $h(f(x)) = 0$ and $h(g(x)) = 1$. Therefore, $h\circ f \ne h\circ g$.'
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'The unit interval $[0, 1]$ is a cogenerator: Suppose we have $f, g : X \rightrightarrows Y$ with $f \ne g$. Choose $x\in X$ such that $f(x) \ne g(x)$. Then by Urysohn''s lemma, there is a continuous function $h : Y \to [0, 1]$ such that $h(f(x)) = 0$ and $h(g(x)) = 1$. Therefore, $h\circ f \ne h\circ g$.'
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),
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(
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'CompHaus',

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