In this note we define the notions of normal subcrossed module and quotient crossed module within groups with opera-tions; and give same results on these crossed modules.
REFERENCES
1.
Akız
, H.F.
, Alemdar
, N.
, Mucuk
O.
, Şahan
T.
, Coverings of internal groupoids and crossed modules in the category of groups with operations
, Georgian Math. Journal
, 20
(2
), 223
–238
, (2013
).2.
Brown
, R.
, Higher dimensional group theory. In: Low Dimensional Topology
, London Math. Soc. Lect. Notes
, 48
, pp. 215
–238
. Cambridge Univ. Press, (1982
).3.
Brown
, R.
, Groupoids and crossed objects in algebraic topology
, Homology Homotopy Appl.
1
, 1
–78
, (1999
).4.
Brown
, R.
, Huebschmann
, J.
, Identities among relations. In: Low Dimentional Topology
, London Math. Soc. Lect. Notes
, 48
, pp. 153
–202
. Cambridge Univ. Press (1982
)5.
Brown
, R.
, Mucuk
, O.
, Covering groups of non-connected topological groups revisited
, Math. Proc. Camb. Phil. Soc.
115
, 97
–110
, (1994
).6.
Brown
, R.
, Spencer
C. B.
, G-groupoids, crossed modules and the fundamental groupoid of a topological group
, Proc. Konn. Ned. Akad. v. Wet.
79
, 296
–302
, (1976
).7.
Datuashvili
, T.
, Categorical, homological and homotopical properties of algebraic objects
, Dissertation, Georgian Academy of Science, Tbilisi
(2006
).8.
Datuashvili
, T.
, Cohomologically trivial internal categories in categories of groups with operations
, Appl. Categ. Structures
3
, 221
–237
, (1995
).9.
Datuashvili
, T.
, Cohomology of internal categories in categories of groups with operations, Categorical Topology and its Relation to Analysis, algebra and combinatorics, Ed. J.
Adamek
and S.
MacLane
(Prague, 1988), World Sci. Publishing
, Teaneck, NJ
, (1989
).10.
Datuashvili
, T.
, Kan extensions of internal functors: Nonconnected case
, J. Pure Appl. Algebra
167
, 195
–202
, (2002
).11.
Datuashvili
, T.
, Whitehead homotopy equivalence and internal category equivalence of crossed modules in categories of groups with operations
, Proc. A. Razmadze Math. Inst.
113
, 3
–30
, (1995
).12.
Higgins
, P.J.
, Groups with multiple operators
, Proc. London Math. Soc.
3
(6
) 366
–416
, (1956
).13.
Huebschmann
, J.
, Crossed n-fold extensions of groups and cohomology
, Comment. Math. Helvetici
55
, 302
–313
, (1980
).14.
Loday
, J.-L.
, Cohomologie et groupes de Steinberg relatifs
, J. Algebra
54
, 178
–202
, (1978
).15.
Loday
, J.-L.
, Spaces with finitely many non-trivial homotopy groups
, J. Pure Appl. Algebra
24
, 179
–202
, (1982
).16.
Lue
, A.S.T.
, Cohomology of groups relative to a variety
, J. Algebra
69
, 155
–174
, (1981
).17.
Mucuk
, O.
, Kılıçarslan
, B.
, Şahan
T.
, Alemdar
, N.
, Group-groupoids and monodromy groupoids
, Topology Appl.
158
(15
), 2034
–2042
, (2011
).18.
Mucuk
, O.
, Şahan
, T.
, Alemdar
, N.
, Normality and quotients in crossed modules and group-groupoids
, Appl. Categor. Struct.
23
, 415
–428
, (2015
).19.
Mucuk
, O.
, Şahan
, T.
, Coverings and crossed modules of topological groups with operations
, Turk. J. Math.
38
(5
), 833
–845
, (2014
).20.
Mucuk
, O.
, Akız
, H. F.
, Monodromy groupoids of an internal groupoid in topological groups with operations
, Filomat
29
(10
), 2355
–2366
, (2015
).21.
Orzech
, G.
, Obstruction theory in algebraic categories I, II
, J. Pure Appl. Algebra
2
, 287–314
, 315
–340
, (1972
).22.
Norrie
, K.
, Actions and Automorphisms of crossed modules
, Bull. Soc. Math. France
, 118
, 129
–146
, (1990
).23.
Porter
, T.
, Extensions, crossed modules and internal categories in categories of groups with operations
, Proc. Edinb. Math. Soc.
30
, 373
–381
, (1987
).24.
Whitehead
, J.H.C.
, Note on a previous paper entitled “On adding relations to homotopy group”
, Ann. of Math.
47
, 806
–810
, (1946
).25.
Whitehead
, J.H.C.
, Combinatorial homotopy II
, Bull. Amer. Math. Soc.
55
, 453
–496
, (1949
).
This content is only available via PDF.
© 2019 Author(s).
2019
Author(s)