# Derived crossed modules

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[1] H. F. Akız, O. Mucuk, N. Alemdar and T. S ̧ahan, Coverings of internal groupoids and crossed modules in the category of groups with operations, Georgian Math. J. 20 (2) (2013), 223–238. Google Scholar

[2] J. C. Baez and D. Stevenson, The Classifying Space of a Topological 2-Group, pages 1–31. Algebraic Topology. Abel Symposia. Springer, 2009. Google Scholar

[3] R. Brown, Groupoids and crossed objects in algebraic topology Homol. Homotopy Appl. 1 (1999), 1–78. Google Scholar

[4] R. Brown and J. Huebschmann, Identities among relations, pages 153–202. Lon- don Mathematical Society Lecture Note Series. Cambridge University Press, 1982. Google Scholar

[5] R. Brown and C. B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Indagat. Math. 79 (4) (1976), 296–302. Google Scholar

[6] W. H. Cockcroft, On the homomorphisms of sequences, Math. Proc. Cambridge 48 (4) (1952), 521–532. Google Scholar

[7] T. Datuashvili, Cohomologically trivial internal categories in categories of groups with operations, Appl. Categor. Struct. 3 (3) (1995), 221–237. Google Scholar

[8] T. Datuashvili. Categorical, homological and homotopical properties of algebraic objects. Dissertation, Georgian Academy of Science, 2006. Google Scholar

[9] J. Huebschmann, Crossed n-folds extensions of groups and cohomology, Comment. Math. Helv. 55 (1980), 302–313. Google Scholar

[10] J.-L. Loday, Cohomologie et groupe de steinberg relatifs, J. Algebra 54 (1) (1978), 178–202. Google Scholar

[11] A. S.-T. Lue, Cohomology of groups relative to a variety, J. Algebra 69 (1) (1981), 155–174. Google Scholar

[12] O. Mucuk and H.F. Akız, Monodromy groupoid of an internal groupoid in topological groups with operations, Filomat 29 (10), (2015), 2355–2366. Google Scholar

[13] O. Mucuk and H. C ̧ akallı, G-connectedness in topological groups with operations, 1079-1089 Filomat 32 (3), (2018), 1079–1089. Google Scholar

[14] O. Mucuk and T. S ̧ahan, Coverings and crossed modules of topological groups with operations, Turk. J. Math. 38 (5) (2014), 833–845. Google Scholar

[15] K. Norrie, Actions and automorphisms of crossed modules, Bull. Soc. Math. Fr. 118 (2) (1990), 129–146. Google Scholar

[16] G. Orzech, Obstruction theory in algebraic categories, I, J. Pure. Appl. Algebra 2 (4) (1972), 287–314. Google Scholar

[17] G. Orzech, Obstruction theory in algebraic categories, II, J. Pure. Appl. Algebra 2 (4) (1972), 315–340. Google Scholar

[18] A. Patchkoria, Crossed semimodules and schreier internal categories in the cat- egory of monoids, Georgian Math. J. 5 (6) (1998), 575–581. Google Scholar

[19] T. Porter, Extensions, crossed modules and internal categories in categories of groups with operations P. Edinburgh. Math. Soc. 30 (3) (1987), 373–381. Google Scholar

[20] T. S ̧ahan, Further remarks on liftings of crossed modules, Hacet. J. Math. Stat., Retrieved 4 Mar. 2018, from Doi: 10.15672/HJMS.2018.554. Google Scholar

[21] S. Temel, Topological crossed semimodules and schreier internal categories in the category of topological monoids, Gazi Univ. J. Sci. 29 (4) (2016), 915–921. Google Scholar

[22] S. Temel, Crossed semimodules of categories and Schreier 2-categories, Tbilisi Math. J. 11 (2) (2018), 47–57. Google Scholar

[23] J. H. C. Whitehead, Note on a previous paper entitled " on adding relations to homotopy groups" , Ann. Math. 47 (4) (1946), 806–810. Google Scholar

[24] J. H. C. Whitehead, On operators in relative homotopy groups, Ann. Math. 49 (3) (1948), 610–640. Google Scholar

[25] J. H. C. Whitehead, Combinatorial homotopy. II, Bull. Amer. Math. Soc. 55 (5) (1949), 453–496. Google Scholar