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Copy file name to clipboardExpand all lines: databases/catdat/data/categories/SemiGrp.yaml
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@@ -75,7 +75,7 @@ unsatisfied_properties:
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reason: >-
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Assume that a natural numbers object exists. Then by <a href="/lemma/nno_distributive_criterion">this result</a>, for every semigroup $A$ the natural homomorphism
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$$\textstyle\alpha : \coprod_{n \geq 0} A \to A \times \coprod_{n \geq 0} 1$$
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is a split monomorphism. But this is not true: For each $n \geq 0$ let $A_n$ denote a copy of $A$. The elements of the coproduct in $\alpha$''s domain have a unique representation as
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is a split monomorphism. But this is not true: For each $n \geq 0$ let $A_n$ denote a copy of $A$. The elements of the coproduct in $\alpha$'s domain have a unique representation as
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$$x_{n_1} * \cdots * x_{n_s}$$
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with $x_i \in A_i$ and $n_i \neq n_{i+1}$, and we have
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