@article {CCH,
    AUTHOR = {Alonso \'Alvarez, J. N. and Fern\'andez Vilaboa, J. M. and
              Gonz\'alez Rodr\'{\i}guez, R.},
     TITLE = {On the (co)commutativity class of a~{H}opf algebra and crossed
              products in a~braided category},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {29},
      YEAR = {2001},
    NUMBER = {12},
     PAGES = {5857--5878},
       DOI = {10.1081/AGB-100107962},
       URL = {https://doi.org/10.1081/AGB-100107962},
}

@article {TAC,
    AUTHOR = {Alonso \'Alvarez, J. N. and Fern\'andez Vilaboa, J. M. and
              Gonz\'alez Rodr\'{\i}guez, R.},
     TITLE = {Crossed products of crossed modules of {H}opf monoids},
   JOURNAL = {Theory Appl. Categ.},
  FJOURNAL = {Theory and Applications of Categories},
    VOLUME = {33},
      YEAR = {2018},
     PAGES = {867--897},
}

@article {AGV,
    AUTHOR = {Angiono, Iv\'an and Galindo, C\'esar and Vendramin, Leandro},
     TITLE = {Hopf braces and {Y}ang--{B}axter operators},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {145},
      YEAR = {2017},
    NUMBER = {5},
     PAGES = {1981--1995},
       DOI = {10.1090/proc/13395},
       URL = {https://doi.org/10.1090/proc/13395},
    EPRINT = {1604.02098},
}

@article {BAXRB,
    AUTHOR = {Baxter, Glen},
     TITLE = {An analytic problem whose solution follows from a~simple
              algebraic identity},
   JOURNAL = {Pacific J.~Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {10},
      YEAR = {1960},
    NUMBER = {3},
     PAGES = {731--742},
       DOI = {10.2140/pjm.1960.10.731},
       URL = {https://doi.org/10.2140/pjm.1960.10.731},
}

@article {BRZ1,
    AUTHOR = {Brzezi\'nski, Tomasz},
     TITLE = {Trusses: {B}etween braces and rings},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {372},
      YEAR = {2019},
    NUMBER = {6},
     PAGES = {4149--4176},
       DOI = {10.1090/tran/7705},
       URL = {https://doi.org/10.1090/tran/7705},
    EPRINT = {1710.02870},
}

@incollection {DR1,
    AUTHOR = {Drinfeld, V. G.},
     TITLE = {On some unsolved problems in quantum group theory},
 BOOKTITLE = {Quantum Groups ({L}eningrad, 1990)},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {1510},
     PAGES = {1--8},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1992},
       DOI = {10.1007/BFb0101175},
       URL = {https://doi.org/10.1007/BFb0101175},
}

@article {Faria,
    AUTHOR = {Faria Martins, Jo\~ao},
     TITLE = {Crossed modules of {H}opf algebras and of associative algebras
              and two-dimensional holonomy},
   JOURNAL = {J.~Geom. Phys.},
  FJOURNAL = {Journal of Geometry and Physics},
    VOLUME = {99},
      YEAR = {2016},
     PAGES = {68--110},
       DOI = {10.1016/j.geomphys.2015.09.012},
       URL = {https://doi.org/10.1016/j.geomphys.2015.09.012},
    EPRINT = {1503.05888},
}

@article {FGR,
    AUTHOR = {Fern\'andez Vilaboa, Jos\'e Manuel and Gonz\'alez Rodr\'{\i}guez,
              Ram\'on and Ramos P\'erez, Brais},
     TITLE = {Categorical isomorphisms for Hopf braces},
   JOURNAL = {Hacet.~J.~Math. Stat.},
  FJOURNAL = {Hacettepe Journal of Mathematics and Statistics},
      NOTE = {{t}o appear},
    EPRINT = {2311.05235},
}

@mics {FSCI,
    AUTHOR = {Ferri, Davide and Sciandra, Andrea},
     TITLE = {Matched pairs and {Y}etter--{D}rinfeld braces},
    EPRINT = {2406.10009},
}

@article {FW,
    AUTHOR = {Fr\'egier, Ya\"el and Wagemann, Friedrich},
     TITLE = {On {H}opf 2-algebras},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2011},
    VOLUME = {2011},
    NUMBER = {15},
     PAGES = {3471--3501},
       DOI = {10.1093/imrn/rnq224},
       URL = {https://doi.org/10.1093/imrn/rnq224},
    EPRINT = {0908.2353},
}

@article {Goncharov,
    AUTHOR = {Goncharov, Maxim},
     TITLE = {Rota--{B}axter operators on cocommutative {H}opf algebras},
   JOURNAL = {J.~Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {582},
      YEAR = {2021},
     PAGES = {39--56},
       DOI = {10.1016/j.jalgebra.2021.04.024},
       URL = {https://doi.org/10.1016/j.jalgebra.2021.04.024},
    EPRINT = {2011.14390},
}

@mics {GONROD,
    AUTHOR = {Gonz\'alez Rodr\'{\i}guez, Ram\'on and Rodr\'{\i}guez Raposo,
              Ana Bel\'en},
     TITLE = {Categorical equivalences for Hopf trusses and their modules},
    EPRINT = {2312.06520},
}

@article {GV,
    AUTHOR = {Guarnieri, L. and Vendramin, L.},
     TITLE = {Skew braces and the {Y}ang--{B}axter equation},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {86},
      YEAR = {2017},
    NUMBER = {307},
     PAGES = {2519--2534},
       DOI = {10.1090/mcom/3161},
       URL = {https://doi.org/10.1090/mcom/3161},
    EPRINT = {1511.03171},
}

@article {JS2,
    AUTHOR = {Joyal, Andr\'e and Street, Ross},
     TITLE = {Braided tensor categories},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {102},
      YEAR = {1993},
    NUMBER = {1},
     PAGES = {20--78},
       DOI = {10.1006/aima.1993.1055},
       URL = {https://doi.org/10.1006/aima.1993.1055},
}

@book {K,
    AUTHOR = {Kassel, Christian},
     TITLE = {Quantum groups},
    SERIES = {Grad. Texts in Math.},
    VOLUME = {155},
 PUBLISHER = {Springer, New York},
      YEAR = {1995},
     PAGES = {xii+531},
       DOI = {10.1007/978-1-4612-0783-2},
       URL = {https://doi.org/10.1007/978-1-4612-0783-2},
}

@article {LST,
    AUTHOR = {Li, Yunnan and Sheng, Yunhe and Tang, Rong},
     TITLE = {Post-{H}opf algebras, relative {R}ota--{B}axter operators and
              solutions to the {Y}ang--{B}axter equation},
   JOURNAL = {J.~Noncommut. Geom.},
  FJOURNAL = {Journal of Noncommutative Geometry},
    VOLUME = {18},
      YEAR = {2024},
    NUMBER = {2},
     PAGES = {605--630},
       DOI = {10.4171/jncg/537},
       URL = {https://doi.org/10.4171/jncg/537},
    EPRINT = {2203.12174},
}

@article {LW,
    AUTHOR = {Li, Zhonghua and Wang, Shukun},
     TITLE = {Rota--{B}axter systems and skew trusses},
   JOURNAL = {J.~Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {623},
      YEAR = {2023},
     PAGES = {447--480},
       DOI = {10.1016/j.jalgebra.2023.02.022},
       URL = {https://doi.org/10.1016/j.jalgebra.2023.02.022},
    EPRINT = {2210.14569},
}

@mics {LW2,
    AUTHOR = {Li, Zhonghua and Wang, Shukun},
     TITLE = {{R}ota--{B}axter systems of {H}opf algebras and {H}opf trusses},
    EPRINT = {2305.00482},
}

@article {LP,
    AUTHOR = {L\'opez L\'opez, M. Purificaci\'on and Villanueva N\'ovoa, Emilio},
     TITLE = {The antipode and the (co)invariants of a~finite {H}opf
              (co)quasigroup},
   JOURNAL = {Appl. Categ. Structures},
  FJOURNAL = {Applied Categorical Structures. A Journal Devoted to
              Applications of Categorical Methods in Algebra, Analysis,
              Computer Science, Logic, Order and Topology},
    VOLUME = {21},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {237--247},
       DOI = {10.1007/s10485-011-9260-5},
       URL = {https://doi.org/10.1007/s10485-011-9260-5},
}

@book {Mac,
    AUTHOR = {Mac Lane, Saunders},
     TITLE = {Categories for the working mathematician},
    SERIES = {Grad. Texts in Math.},
    VOLUME = {5},
   EDITION = {Second},
 PUBLISHER = {Springer, New York},
      YEAR = {1978},
     PAGES = {xii+318},
       DOI = {10.1007/978-1-4757-4721-8},
       URL = {https://doi.org/10.1007/978-1-4757-4721-8},
}

@article {M1990,
    AUTHOR = {Majid, Shahn},
     TITLE = {Physics for algebraists: {N}oncommutative and noncocommutative
              {H}opf algebras by a~bicrossproduct construction},
   JOURNAL = {J.~Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {130},
      YEAR = {1990},
    NUMBER = {1},
     PAGES = {17--64},
       DOI = {10.1016/0021-8693(90)90099-A},
       URL = {https://doi.org/10.1016/0021-8693(90)90099-A},
}

@book {M1995,
    AUTHOR = {Majid, Shahn},
     TITLE = {Foundations of quantum group theory},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1995},
     PAGES = {x+607},
       DOI = {10.1017/CBO9780511613104},
       URL = {https://doi.org/10.1017/CBO9780511613104},
}

@mics {MA2,
    AUTHOR = {Majid, Shahn},
     TITLE = {Strict quantum 2-groups},
    EPRINT = {1208.6265},
}

@article {Molnar,
    AUTHOR = {Molnar, Richard K.},
     TITLE = {Semi-direct products of {H}opf algebras},
   JOURNAL = {J.~Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {47},
      YEAR = {1977},
    NUMBER = {1},
     PAGES = {29--51},
       DOI = {10.1016/0021-8693(77)90208-3},
       URL = {https://doi.org/10.1016/0021-8693(77)90208-3},
}

@article {RORB,
    AUTHOR = {Rota, Gian-Carlo},
     TITLE = {Baxter algebras and combinatorial identities.~{I}},
   JOURNAL = {Bull. Amer. Math. Soc.},
  FJOURNAL = {Bulletin of the American Mathematical Society},
    VOLUME = {75},
      YEAR = {1969},
     PAGES = {325--329},
       DOI = {10.1090/S0002-9904-1969-12156-7},
       URL = {https://doi.org/10.1090/S0002-9904-1969-12156-7},
}

@article {Rump,
    AUTHOR = {Rump, Wolfgang},
     TITLE = {Braces, radical rings, and the quantum {Y}ang--{B}axter
              equation},
   JOURNAL = {J.~Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {307},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {153--170},
       DOI = {10.1016/j.jalgebra.2006.03.040},
       URL = {https://doi.org/10.1016/j.jalgebra.2006.03.040},
}

@article {Sch,
    AUTHOR = {Schauenburg, Peter},
     TITLE = {On the braiding on a~{H}opf algebra in a~braided category},
   JOURNAL = {New York J.~Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {4},
      YEAR = {1998},
     PAGES = {259--263},
}

@mics {SCI,
    AUTHOR = {Sciandra, Andrea},
     TITLE = {{Y}etter--{D}rinfeld post-Hopf algebras and {Y}etter--{D}rinfeld relative
              {R}ota--{B}axter opertors},
    EPRINT = {2407.17922},
}

@mics {Wang,
    AUTHOR = {Wang, Shukun},
     TITLE = {(Weak) twisted post-groups, skew trusses and rings},
    EPRINT = {2307.10535},
}
