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<p>We prove that for any bisimplicial set <i>X</i>, the natural comparison map between the diagonal <i>dX</i> and the total simplicial set <i>TX</i> is a categorical equivalence in the sense of Joyal and Lurie.</p>

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A remark on the total simplicial set functor

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月9日

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  • Danny Stevenson

摘要

We prove that for any bisimplicial set X, the natural comparison map between the diagonal dX and the total simplicial set TX is a categorical equivalence in the sense of Joyal and Lurie.