Pushouts of profinite crossed modules and $cat^1$ -profinite groups
Pushouts of profinite crossed modules and $cat^1$ -profinite groups
In this paper, we presented a brief review of crossed modules [7], $cat^1$ -groups [6], pullback crossed modules [4], pullback $cat^1$ -group [1], profinite crossed modules [5], $cat^1$ -profinite groups [5], pullback profinite crossed modules [5], pullback $cat^1$ -profinite groups [3]. We defined the pushout $cat^1$ -profinite groups and gave the left adjoint constructions.
___
- [1] Alp, M., Pullbacks of Crossed modules and Cat1-groups, Turkish journal of Mathematics, (3) 22, 273-281, (1998).
- [2] Alp, M., Left adjoint of pullback cat1-profinite groups, Turkish journal of Mathematics, (2) 26, 159-167, (2002).
- [3] Alp, M., Pullbacks of Profinite Crossed modules and cat1-profinite groups, Algebras, Groups and Geometries, (To appear).
- [4] Brown, R., and Higgins, P.J., On the connection between the second relative homotopy groups of some related space, Proc. London Math. Soc., (3) 36, 193-212, (1978).
- [5] Korkes , F. J., and Porter, T., Profinite crossed modules, U. W. B. Pure Mathematics Preprint No. 86.11, pp. 1-37, (1986).
- [6] Loday, J. L., Spaces with finitely many non-trivial homotopy groups, J.App.Algebra, 24 179-202, (1982).
- [7] Whitehead, J. H. C., Combinatorial homotopy II, Bull. Amer. Mat. Soc., 55, 453-496, (1949).