Some remarks on MCI crossed modules

In an earlier work, it is proven that the category of crossed modules in a modified category of interest (MCI crossed modules) is finitely complete with a certain condition, in which all codomains are fixed. In this paper, we prove that this is also true without any restriction.

[1]  I. Akça,et al.  Completeness of the Category of Rack Crossed Modules , 2022, Ikonion Journal of Mathematics.

[2]  A. Salemkar,et al.  The category of generalized crossed modules , 2018 .

[3]  Kadir Emir,et al.  Limits in Modified Categories of Interest , 2017, 1805.04877.

[4]  Kadir Emir,et al.  Pullback crossed modules in the category of racks , 2016, 1611.07007.

[5]  Ronald Brown Modelling and Computing Homotopy Types: I , 2016, 1610.07421.

[6]  Tunçar Şahan,et al.  Group-groupoid actions and liftings of crossed modules , 2016, Georgian Mathematical Journal.

[7]  M. Ladra,et al.  More on crossed modules of Lie, Leibniz, associative and diassociative algebras , 2015, 1508.01147.

[8]  João F. Martins Crossed modules of Hopf algebras and of associative algebras and two-dimensional holonomy , 2015, 1503.05888.

[9]  Alissa S. Crans,et al.  Crossed modules of racks , 2013, 1310.4705.

[10]  A. Aytekin,et al.  SEMI-COMPLETE CROSSED MODULES OF LIE ALGEBRAS , 2012 .

[11]  T. Porter Extensions, crossed modules and internal categories in categories of groups with operations , 1987, Proceedings of the Edinburgh Mathematical Society.

[12]  G. Orzech Obstruction theory in algebraic categories, I☆ , 1972 .

[13]  P. J. Higgins Groups with Multiple Operators , 1956 .

[14]  J. Whitehead,et al.  On Adding Relations to Homotopy Groups , 1941 .

[15]  A. Aytekin,et al.  Colimits of crossed modules in modified categories of interest , 2020, Electronic Research Archive.

[16]  J. Casas,et al.  ACTIONS IN MODIFIED CATEGORIES OF INTEREST WITH APPLICATION TO CROSSED MODULES Dedicated to Teimuraz Pirashvili on his 60th birthday , 2015 .

[17]  B. Davvaz,et al.  CROSSED POLYMODULES AND FUNDAMENTAL RELATIONS , 2015 .