Natural transformations for quasigroupoids

References

[1] E. Abe, Hopf Algebras, Cambridge Tracts in Math. 74, Cambridge University, Cambridge, 1980. Search in Google Scholar

[2] J. N. Alonso Álvarez, J. M. Fernández Vilaboa and R. González Rodríguez, A characterization of weak Hopf (co) quasigroups, Mediterr. J. Math. 13 (2016), no. 5, 3747–3764. 10.1007/s00009-016-0712-xSearch in Google Scholar

[3] J. N. Alonso Álvarez, J. M. Fernández Vilaboa and R. González Rodríguez, Cleft and Galois extensions associated with a weak Hopf quasigroup, J. Pure Appl. Algebra 220 (2016), no. 3, 1002–1034. 10.1016/j.jpaa.2015.08.005Search in Google Scholar

[4] J. N. Alonso Álvarez, J. M. Fernández Vilaboa and R. González Rodríguez, Weak Hopf quasigroups, Asian J. Math. 20 (2016), no. 4, 665–693. 10.4310/AJM.2016.v20.n4.a4Search in Google Scholar

[5] J. N. Alonso Álvarez, J. M. Fernández Vilaboa and R. González Rodríguez, Quasigroupoids and weak Hopf quasigroups, J. Algebra 568 (2021), 408–436. 10.1016/j.jalgebra.2020.10.011Search in Google Scholar

[6] J. Bénabou, Introduction to bicategories, Reports of the Midwest Category Seminar, Springer, Berlin (1967), 1–77. 10.1007/BFb0074299Search in Google Scholar

[7] G. Böhm, J. Gómez-Torrecillas and E. López-Centella, On the category of weak bialgebras, J. Algebra 399 (2014), 801–844. 10.1016/j.jalgebra.2013.09.032Search in Google Scholar

[8] G. Böhm, F. Nill and K. Szlachányi, Weak Hopf algebras. I. Integral theory and C * -structure, J. Algebra 221 (1999), no. 2, 385–438. 10.1006/jabr.1999.7984Search in Google Scholar

[9] H. Brandt, Über eine Verallgemeinerung des Gruppenbegriffes, Math. Ann. 96 (1927), no. 1, 360–366. 10.1007/BF01209171Search in Google Scholar

[10] R. H. Bruck, Contributions to the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245–354. 10.1090/S0002-9947-1946-0017288-3Search in Google Scholar

[11] O. Chein, Moufang loops of small order. I, Trans. Amer. Math. Soc. 188 (1974), 31–51. 10.1090/S0002-9947-1974-0330336-3Search in Google Scholar

[12] S. Eilenberg and S. MacLane, Natural isomorphisms in group theory, Proc. Natl. Acad. Sci. USA 28 (1942), 537–543. 10.1073/pnas.28.12.537Search in Google Scholar PubMed PubMed Central

[13] S. Eilenberg and S. MacLane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231–294. 10.1090/S0002-9947-1945-0013131-6Search in Google Scholar

[14] P. Etingof, D. Nikshych and V. Ostrik, On fusion categories, Ann. of Math. (2) 162 (2005), no. 2, 581–642. 10.4007/annals.2005.162.581Search in Google Scholar

[15] J. Grabowski, An introduction to loopoids, Comment. Math. Univ. Carolin. 57 (2016), no. 4, 515–526. 10.14712/1213-7243.2015.184Search in Google Scholar

[16] J. Grabowski and Z. Ravanpak, Nonassociative analogs of Lie groupoids, Differential Geom. Appl. 82 (2022), Paper No. 101887. 10.1016/j.difgeo.2022.101887Search in Google Scholar

[17] P. Hahn, Haar measure for measure groupoids, Trans. Amer. Math. Soc. 242 (1978), 1–33. 10.1090/S0002-9947-1978-0496796-6Search in Google Scholar

[18] T. Hayashi, Face algebras. I. A generalization of quantum group theory, J. Math. Soc. Japan 50 (1998), no. 2, 293–315. 10.2969/jmsj/05020293Search in Google Scholar

[19] J. Klim and S. Majid, Hopf quasigroups and the algebraic 7-sphere, J. Algebra 323 (2010), no. 11, 3067–3110. 10.1016/j.jalgebra.2010.03.011Search in Google Scholar

[20] D. Nikshych and L. Vainerman, Finite quantum groupoids and their applications, New Directions in Hopf Algebras, Math. Sci. Res. Inst. Publ. 43, Cambridge University, Cambridge (2002), 211–262. Search in Google Scholar

[21] T. Yamanouchi, Duality for generalized Kac algebras and a characterization of finite groupoid algebras, J. Algebra 163 (1994), no. 1, 9–50. 10.1006/jabr.1994.1002Search in Google Scholar