| 總結: | Let <i>H</i> be a crossed group-cograded Hopf quasigroup. We first introduce the notion of <i>p</i>-Yetter–Drinfeld quasimodule over <i>H</i>. If the antipode of <i>H</i> is bijective, we show that the category <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Y</mi><mi>D</mi><mi>Q</mi><mo>(</mo><mi>H</mi><mo>)</mo></mrow></semantics></math></inline-formula> of Yetter–Drinfeld quasimodules over <i>H</i> is a crossed category, and the subcategory <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Y</mi><mi>D</mi><mo>(</mo><mi>H</mi><mo>)</mo></mrow></semantics></math></inline-formula> of Yetter–Drinfeld modules is a braided crossed category.
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