本课题主要研究与pseudo-双代数相关的杨巴克斯特方程和上同调理论以及范畴化问题。我们首先研究李pseudo-(双)代数的范畴化和量子化问题；利用李2-pseudo-代数上的O-算子构造2-分次CYBE的解。其次，计算一些特殊的李pseudo-代数的上同调，考虑左对称pseudo-代数、李2-pseudo-代数、李pseudo-双代数和无穷小pseudo-双代数的上同调理论。最后，证明parakahler型李pseudo-代数与左对称pseudo-双代数等价，探究预交错pseudo-双代数与交错pseudo-代数的相空间的等价性，系统地研究左对称pseudo-双代数意义下的S-方程，预交错pseudo-双代数体数系下的PA-方程和交错pseudo-代数意义下的AYBE。

This project mainly studies theories of YBE, cohomology and categorification on pseudo-bialgebra. We are firstly devoted to considering the categorification and quantization of Lie pseudo-bialgebra and constructing the solutions of the 2-graded CYBE in the strict Lie 2-pseudoalgebra using O-operators . Secondly, we compute the cohomology of some special Lie pseudoalgebra and consider the cohomology theory of left symmetric pseudoalgebra, Lie 2-pseudoalgebra, Lie pseudo-bialgebra and infinitesimal pseudo-bialgebra. Finally, we prove that left symmetric pseudo-bialgebra is equivalent to parakahler Lie pseudoalgebra; we also explore the equivalence between the phase space of alternative pseudoalgebra and prealternative pseudo-bialgebra. Furthermore, the S-equation in the sense of left symmetric pseudo-bialgebra, PA-equation of prealternative pseudo-bialgebra and AYBE of D-pseudo-bialgebra are also systematically studied.