Pentactions and action representability in the category of reduced groups with action

References

[1] M. Atık, A. Aytekın and E. Uslu, Representability of actions in the category of (pre)crossed modules in Leibniz algebras, Comm. Algebra 45 (2017), no. 5, 1825–1841. 10.1080/00927872.2016.1226853Search in Google Scholar

[2] F. Borceux, G. Janelidze and G. M. Kelly, Internal object actions, Comment. Math. Univ. Carolin. 46 (2005), no. 2, 235–255. Search in Google Scholar

[3] Y. Boyaci, J. M. Casas, T. Datuashvili and E. Ö. Uslu, Actions in modified categories of interest with application to crossed modules, Theory Appl. Categ. 30 (2015), 882–908. Search in Google Scholar

[4] J. M. Casas, T. Datuashvili and M. Ladra, Actors in categories of interest, preprint (2007), https://arxiv.org/abs/math/0702574. Search in Google Scholar

[5] J. M. Casas, T. Datuashvili and M. Ladra, Actor of an alternative algebra, preprint (2009), https://arxiv.org/abs/0910.0550. Search in Google Scholar

[6] J. M. Casas, T. Datuashvili and M. Ladra, Actor of a precrossed module, Comm. Algebra 37 (2009), no. 12, 4516–4541. 10.1080/00927870902829130Search in Google Scholar

[7] J. M. Casas, T. Datuashvili and M. Ladra, Universal strict general actors and actors in categories of interest, Appl. Categ. Structures 18 (2010), no. 1, 85–114. 10.1007/s10485-008-9166-zSearch in Google Scholar

[8] J. M. Casas, T. Datuashvili and M. Ladra, Actor of a Lie–Leibniz algebra, Comm. Algebra 41 (2013), no. 4, 1570–1587. 10.1080/00927872.2011.644608Search in Google Scholar

[9] J. M. Casas, T. Datuashvili and M. Ladra, Action theory of alternative algebras, Georgian Math. J. 26 (2019), no. 2, 177–197. 10.1515/gmj-2019-2015Search in Google Scholar

[10] J. M. Casas, T. Datuashvili, M. Ladra and E. Ö. Uslu, Actions in the category of precrossed modules in Lie algebras, Comm. Algebra 40 (2012), no. 8, 2962–2982. 10.1080/00927872.2011.588632Search in Google Scholar

[11] T. Datuashvili, Central series for groups with action and Leibniz algebras, Georgian Math. J. 9 (2002), no. 4, 671–682. Search in Google Scholar

[12] T. Datuashvili, Witt’s theorem for groups with action and free Leibniz algebras, Georgian Math. J. 11 (2004), no. 4, 691–712. 10.1515/GMJ.2004.691Search in Google Scholar

[13] T. Datuashvili, Categorical, homological, and homotopical properties of algebraic objects, J. Math. Sci. (N. Y.) 225 (2017), no. 3, 383–533. 10.1007/s10958-017-3474-5Search in Google Scholar

[14] T. Datuashvili and T. Şahan, Actions and semi-direct products in categories of groups with action, Hacet. J. Math. Stat. (2023), 10.15672/hujms.1028848. 10.15672/hujms.1028848Search in Google Scholar

[15] J.-L. Loday, Une version non commutative des algèbres de Lie: les algèbres de Leibniz, Enseign. Math. (2) 39 (1993), no. 3–4, 269–293. Search in Google Scholar

[16] J.-L. Loday, Algebraic K-theory and the conjectural Leibniz K-theory, K-Theory 30 (2003), no. 2, 105–127. 10.1023/B:KTHE.0000018382.90150.ceSearch in Google Scholar

[17] G. Orzech, Obstruction theory in algebraic categories. I, J. Pure Appl. Algebra 2 (1972), 287–314. 10.1016/0022-4049(72)90008-4Search in Google Scholar

[18] G. Orzech, Obstruction theory in algebraic categories. II, J. Pure Appl. Algebra 2 (1972), 315–340. 10.1016/0022-4049(72)90009-6Search in Google Scholar

[19] T. Porter, Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edinb. Math. Soc. (2) 30 (1987), no. 3, 373–381. 10.1017/S0013091500026766Search in Google Scholar