Let \(H_1\) and \(H_2\) be Hopf algebras which are not necessarily finite dimensional and \(\alpha ,\beta \in Aut_{Hopf}(H_1),\gamma ,\delta \in Aut_{Hopf}(H_2)\). In this paper, we introduce a category \(_{H_1}\mathcal {LR}_{H_2}(\alpha ,\beta ,\gamma ,\delta )\), generalizing Yetter–Drinfeld–Long bimodules and construct a braided T-category \(\mathcal {LR}(H_1,H_2)\) containing all the categories \(_{H_1}\mathcal {LR}_{H_2}(\alpha ,\beta ,\gamma ,\delta )\) as components. We also prove that if \((\alpha ,\beta ,\gamma ,\delta )\) admits a quadruple in involution, then \(_{H_1}\mathcal {LR}_{H_2}(\alpha ,\beta ,\gamma ,\delta )\) is isomorphic to the usual category \(_{H_1}\mathcal {LR}_{H_2}\) of Yetter–Drinfeld–Long bimodules.

令\（H_1 \）和\（H_2 \）为Hopf代数，它们不一定是有限维的，而\（\ alpha，\ beta \ in Aut_ {Hopf}（H_1），\ gamma，\ delta \ in Aut_ {Hopf} （H_2）\）。在本文中，我们介绍了一个类别\（_ {H_1} \ mathcal {LR} _ {H_2}（\ alpha，\ beta，\ gamma，\ delta）\），推广了Butter–Drinfeld–Long双模并构造了一个编织Ť -category \（\ mathcal {LR}（H_1，H_2）\）包含所有的类别\（_ {H_1} \ {mathcal LR} _ {H_2}（\α，\-β，\γ，\三角洲）\ ）作为组件。我们还证明了，如果\（（\ alpha，\ beta，\ gamma，\ delta）\）允许四次对合，那么\（_ {H_1} \ mathcal {LR} _ {H_2}（\ alpha，\ beta，\ gamma，\ delta）\）与通常的类别\（_ {H_1} \ mathcal {LR} _ {H_2 } \）的Yetter–Drinfeld–Long双模。