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    "en": "semigroup homomorphism"
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            "text": "半群同态是保持两边运算的映射；材料用迭代半群给出例子：$\\phi(n)=f^{n}$，并满足：\n\n$$\n\\phi(n+m)=f^{n+m}=f^n\\circ f^m.\n$$\n\n",
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            "conditions": "定义适用于具有结合二元运算的集合；例子中的 $f$ 是集合上的自映射，运算为函数复合。",
            "notation": "$\\hat{\\mathbb{N}}$ 表示含 $0$ 的自然数半群；$E_f$ 表示 $f$ 的演化半群，复合记作 $\\circ$。",
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